Matching Connection Points: Lesson Test

Answer: A

Correct answer: North. Two flat edges can lie against each other only if they face each other, which means pointing in opposite directions. Picture the fixed port facing south: the partner must approach from the south side and face back toward it, so it faces north. A tempting error is matching the same label, south to south, but two edges pointing the same way turn their backs on each other. East or west would leave the ports at right angles.

• A (correct): Touching edges face opposite ways, and the opposite of south is north, so this port can meet the fixed one.
• B: East is only a quarter turn away from south, not its opposite, so the ports would sit at right angles.
• C: West is a quarter turn away from south rather than opposite it, so the edges could not lie against each other.
• D: Two ports that both face south point the same way, so they could never touch along a shared boundary.

Answer: D

Correct answer: North. A clockwise quarter turn moves every edge one step clockwise: north to east, east to south, south to west, and west to north. The mark on the west edge therefore ends up on the north edge.

• A: South is where west goes after a counterclockwise quarter turn, the reverse of the turn described.
• B: East is where west ends up after a half turn of 180 degrees, not a quarter turn.
• C: The mark is printed on the plate and travels with it, so it cannot stay on the west side after a turn.
• D (correct): In a clockwise quarter turn each edge moves one step clockwise, and the step after west is north.

Answer: D

Correct answer: Turning the piece 90 degrees clockwise. Sliding never changes the direction an edge faces, so a turn is required. By the quarter-turn table, a 90 degree clockwise turn changes north into east.

• A: Moving it straight in any direction keeps the port facing north; only a turn changes its direction.
• B: Sliding moves the piece without changing which way any edge faces, so the port would still face north.
• C: A counterclockwise quarter turn sends north to west, the opposite of the direction needed.
• D (correct): A clockwise quarter turn sends north to east, which is exactly the direction needed.

Answer: B

Correct answer: West. A 180 degree turn swaps opposites: north with south and east with west. The mark on the east edge therefore moves to the west edge.

• A: South is where east goes after a single clockwise quarter turn, which is only half of the turn described.
• B (correct): A half turn swaps opposite edges, so the east edge becomes the west edge.
• C: North is where east goes after a counterclockwise quarter turn, not a half turn.
• D: Only a full 360 degree turn returns the mark to the east edge; a half turn moves it.

Answer: B

Correct answer: P, S, R, Q. Every rotation keeps the labels in the same clockwise order, only starting from a different edge. P, S, R, Q runs the labels in reverse order, which is the sign of a mirror image.

• A: This is the original order shifted by three places, so it is a legal turned copy.
• B (correct): This reverses the clockwise order of the labels, which only a reflection can do, so the plate has been flipped.
• C: This is the original order shifted by one place, which is what a quarter turn produces.
• D: This is the original order shifted by two places, which a half turn produces.

Answer: C

Correct answer: 3 units wide and 9 units tall. A turn may swap which side runs across and which runs up, but both lengths stay the same. A rectangle 3 units wide and 9 units tall keeps the 9 and 3 unit sides, so it is the original turned a quarter turn.

• A: The long side has shrunk from 9 to 6 units, changing the 3 to 1 ratio of the original.
• B: The short side has grown from 3 to 4 units, so the piece has been stretched, which is not allowed.
• C (correct): A quarter turn swaps width and height while keeping both lengths, so this is the same rectangle turned.
• D: This is a square, so the short side has been stretched to match the long side.

Answer: A

Correct answer: A slot 4 units wide and 1 unit deep. For a clean joint the slot must be as wide as the tab and as deep as the tab is long. The tab is 4 units wide and 1 unit long, so the slot must be 4 units wide and 1 unit deep.

• A (correct): The slot matches the tab's 4 unit width and 1 unit length, so the tab fills it exactly.
• B: The width matches, but the slot is 1 unit deeper than the tab is long, leaving an empty gap at its bottom.
• C: The slot is 1 unit narrower than the tab, so the tab would hit the slot's walls.
• D: This mixes up width and depth; a 4 unit wide tab cannot enter a 1 unit wide opening.

Answer: D

Correct answer: A tab facing a recess. Matching letters is not enough; connector shapes must complement each other. A protruding tab fits into a recess, pairing out with in.

• A: Two recesses leave an empty gap between the pieces instead of a joint.
• B: A bump against a flat edge cannot sit flush; a bump needs a scoop of the same curve.
• C: Two tabs pointing at each other would both need to fill the same space, so they collide.
• D (correct): A shape that sticks out pairs with a shape that cuts in, so the tab fills the recess.

Answer: D

Correct answer: None at all. Solid pieces may touch along edges or at single points, but they can never occupy the same space. The overlap area must be zero.

• A: Matching labels never excuse overlap; the fit rule must hold along with the label rule.
• B: Tabs fill recesses, not other solid material, so no allowance for overlap exists.
• C: Even a small shared region means solid material is in the same place twice, which makes the choice impossible.
• D (correct): Pieces may touch along edges or at points, but the shared interior area must be exactly zero.

Answer: B

Correct answer: One contact still lets the piece spin around that point. Matching a single point fixes where the piece is but not how it is turned. The piece could still be flipped, changed in shape, or turned so it overlaps, so the rest of the checklist still applies.

• A: One shared point fixes location only; the piece can still spin around that point into a wrong position.
• B (correct): With only one point fixed, the piece could point in many directions, so other details such as shape or overlap must still be checked.
• C: Point contacts are legal; the problem is that one point alone does not fix how the piece is turned.
• D: A mark can sit on an edge, a corner, or inside a piece; where it sits does not make a contact invalid.

Answer: C

Correct answer: 90 degrees counterclockwise. The socket faces north, so the plug must face the opposite way, south. A counterclockwise quarter turn changes west into south, so the loose block turns 90 degrees counterclockwise.

• A: Left alone, the plug faces west, a quarter turn away from the south direction it needs.
• B: A half turn sends west to east, which is sideways to the socket rather than facing it.
• C (correct): The plug must face south, and a counterclockwise quarter turn sends west to south.
• D: A clockwise quarter turn sends west to north, so the plug would point away from the socket.

Answer: B

Correct answer: (G, K, A, D). A half turn swaps north with south and east with west. G, the old south mark, moves to north; K moves from west to east; A moves to south; and D moves to west, giving (G, K, A, D).

• A: This reverses the clockwise order, which describes a flipped plate rather than any rotation.
• B (correct): A half turn shifts every mark two places, so the old south mark G is now on the north edge.
• C: This is the result of a counterclockwise quarter turn, a shift by one place the other way.
• D: This is a shift by one place, which is what a clockwise quarter turn gives, not a half turn.

Answer: B

Correct answer: 5 units east of C. The pivot C stays in place and D keeps its 5 unit distance. A clockwise quarter turn changes north into east, so D ends 5 units east of C.

• A: The direction is right, but every point keeps its distance from the pivot, so D stays 5 units away.
• B (correct): Clockwise, north becomes east, and D keeps its 5 unit distance from the pivot.
• C: South is where north goes after a half turn, which is twice the turn described.
• D: West is where north goes after a counterclockwise quarter turn, the wrong direction.

Answer: A

Correct answer: 5 units. Both pairs can meet only if the K to R distance is the same on both pieces. On piece 1 that distance is

units, so piece 2 needs K and R 5 units apart.

• A (correct): Rigid pieces keep their spacing, and the K to R spacing on piece 1 is 7 - 2 = 5 units.
• B: This adds the two corner distances instead of subtracting them.
• C: This is R's distance from the corner, not the spacing between K and R.
• D: This is K's distance from the corner, not the distance between the two marks.

Answer: A

Correct answer: 4 units. A mark keeps its fractional position on its own edge after a turn. One third of 12 units is

units, so the dot stays 4 units from the same corner.

• A (correct): One third of 12 is 4, and the mark travels with the piece, so it stays 4 units from the same corner.
• B: This is the dot's distance from the other end of the edge, not from the corner named.
• C: This uses the 3 from one third as a distance instead of finding one third of 12.
• D: This places the dot at the middle of the edge, the classic slid-dot decoy.

Answer: C

Correct answer: A half-circle scoop with a 6 unit opening. A bump pairs with a scoop of the same radius bending the opposite way. A half circle of radius 3 spans 2r = 2 x 3 = 6 units, so the scoop must be a half circle with a 6 unit opening.

• A: Two bumps both bulge outward, so they cannot nest into each other.
• B: This opening is 3 units too wide, which would leave gaps around the bump.
• C (correct): A scoop caves in to match the bump, and its opening equals the bump's full width of 2 x 3 = 6 units.
• D: A 3 unit opening matches the radius, not the full width of the bump, so the bump would hit its edges.

Answer: C

Correct answer: 2.5 units. A circle resting on a straight edge touches it at one point, so its center is exactly one radius away. The radius is 2.5 units, so the center is 2.5 units from the edge.

• A: This is half the radius, so the circle's rim would cut through the edge and overlap it.
• B: This is the diameter; at that height the circle would float one radius above the edge.
• C (correct): For a tangent contact the center sits exactly one radius from the edge, which is 2.5 units.
• D: With its center on the edge, half of the circle would cross into the other side.

Answer: D

Correct answer: B first, then A. When two edges meet, the pieces travel their shared boundary in opposite directions. Since piece 1 reads A then B clockwise, piece 2 must read B then A clockwise along its matching edge.

• A: The order matters: the wrong order puts A against B no matter how the piece is turned.
• B: If both pieces read A then B clockwise, the marks can only line up after a flip, which is not allowed.
• C: Two different marks at one spot would mean zero spacing, which cannot match piece 1's spacing.
• D (correct): Joined edges are traced in opposite directions, so a clockwise A then B on one piece needs B then A on the other.

Answer: C

Correct answer: South. The arrow from A to B changed from south to west, which is one clockwise quarter turn. The same turn applies to the whole piece, and a clockwise quarter turn sends east to south, so the notch must be on the south edge.

• A: The notch would stay east only if the piece had not turned, but the arrow changed direction.
• B: North is where east goes after a counterclockwise quarter turn, but the arrow shows a clockwise turn.
• C (correct): The arrow shows a 90 degree clockwise turn, which sends the east edge to the south.
• D: West is where east goes after a half turn; the arrow moved only one quarter step.

Answer: A

Correct answer: Five. In a contact graph, every required contact is its own line between two pieces. W and X share two lines (A and B), and C, D, and E add one line each, for

contacts.

• A (correct): Each named mark is its own required contact: A, B, C, D, and E make five.
• B: This counts one fewer than the number of pieces, as if they formed a simple chain.
• C: This counts the pairs of pieces that touch but treats the two W and X marks as a single contact.
• D: This adds a contact that is not required; a choice showing an extra contact should be rejected.

Answer: C

A's port faces east, so the touching edge of B must face the opposite way, west, and that edge must carry R. B's R starts on its bottom (south) edge, and moving it south to west takes one clockwise quarter turn, so B must turn 90 degrees clockwise. Only that picture puts R on B's joining edge, against A's R.

• A: Turning B 180 degrees clockwise puts the letter M on the joining west edge and leaves R facing north, so the R connectors do not meet.
• B: Leaving B unturned puts the letter T on the joining west edge and leaves R facing south, so the R connectors do not meet.
• C (correct): A 90 degree clockwise turn carries R from B's south edge to its west edge, right against A's R port.
• D: Turning B 270 degrees clockwise puts the letter K on the joining west edge and leaves R facing east, so the R connectors do not meet.

Answer: A

A's port faces north, so the touching edge of B must face the opposite way, south, and that edge must carry M. B's M starts on its top (north) edge, and moving it north to east to south takes two clockwise quarter turns, so B must turn 180 degrees clockwise. Only that picture puts M on B's joining edge, against A's M.

• A (correct): A 180 degree clockwise turn carries M from B's north edge to its south edge, right against A's M port.
• B: Leaving B unturned puts the letter S on the joining south edge and leaves M facing north, so the M connectors do not meet.
• C: Turning B 90 degrees clockwise puts the letter K on the joining south edge and leaves M facing east, so the M connectors do not meet.
• D: Turning B 270 degrees clockwise puts the letter V on the joining south edge and leaves M facing west, so the M connectors do not meet.

Answer: D

A's port faces west, so the touching edge of B must face the opposite way, east, and that edge must carry P. B's P is already on its right (east) edge, so B needs no turn at all; it slides straight into place. Only that picture puts P on B's joining edge, against A's P.

• A: Turning B 270 degrees clockwise puts the letter T on the joining east edge and leaves P facing north, so the P connectors do not meet.
• B: Turning B 90 degrees clockwise puts the letter R on the joining east edge and leaves P facing south, so the P connectors do not meet.
• C: Turning B 180 degrees clockwise puts the letter L on the joining east edge and leaves P facing west, so the P connectors do not meet.
• D (correct): Left unturned, B already has P on its east edge, so it meets A's P port directly.

Answer: A

A's port faces south, so the touching edge of B must face the opposite way, north, and that edge must carry Q. B's Q is already on its top (north) edge, so B needs no turn at all; it slides straight into place. Only that picture puts Q on B's joining edge, against A's Q.

• A (correct): Left unturned, B already has Q on its north edge, so it meets A's Q port directly.
• B: Turning B 180 degrees clockwise puts the letter M on the joining north edge and leaves Q facing south, so the Q connectors do not meet.
• C: Turning B 270 degrees clockwise puts the letter J on the joining north edge and leaves Q facing west, so the Q connectors do not meet.
• D: Turning B 90 degrees clockwise puts the letter R on the joining north edge and leaves Q facing east, so the Q connectors do not meet.

Answer: D

A's port faces north, so the touching edge of B must face the opposite way, south, and that edge must carry X. B's X starts on its right (east) edge, and moving it east to south takes one clockwise quarter turn, so B must turn 90 degrees clockwise. Only that picture puts X on B's joining edge, against A's X.

• A: Leaving B unturned puts the letter N on the joining south edge and leaves X facing east, so the X connectors do not meet.
• B: Turning B 180 degrees clockwise puts the letter B on the joining south edge and leaves X facing west, so the X connectors do not meet.
• C: Turning B 270 degrees clockwise puts the letter C on the joining south edge and leaves X facing north, so the X connectors do not meet.
• D (correct): A 90 degree clockwise turn carries X from B's east edge to its south edge, right against A's X port.

Answer: C

A's port faces east, so the touching edge of B must face the opposite way, west, and that edge must carry H. B's H starts on its right (east) edge, and moving it east to south to west takes two clockwise quarter turns, so B must turn 180 degrees clockwise. Only that picture puts H on B's joining edge, against A's H.

• A: Leaving B unturned puts the letter P on the joining west edge and leaves H facing east, so the H connectors do not meet.
• B: Turning B 270 degrees clockwise puts the letter T on the joining west edge and leaves H facing north, so the H connectors do not meet.
• C (correct): A 180 degree clockwise turn carries H from B's east edge to its west edge, right against A's H port.
• D: Turning B 90 degrees clockwise puts the letter G on the joining west edge and leaves H facing south, so the H connectors do not meet.

Answer: C

A's port faces south, so the touching edge of B must face the opposite way, north, and that edge must carry S. B's S starts on its bottom (south) edge, and moving it south to west to north takes two clockwise quarter turns, so B must turn 180 degrees clockwise. Only that picture puts S on B's joining edge, against A's S.

• A: Leaving B unturned puts the letter H on the joining north edge and leaves S facing south, so the S connectors do not meet.
• B: Turning B 270 degrees clockwise puts the letter L on the joining north edge and leaves S facing east, so the S connectors do not meet.
• C (correct): A 180 degree clockwise turn carries S from B's south edge to its north edge, right against A's S port.
• D: Turning B 90 degrees clockwise puts the letter Y on the joining north edge and leaves S facing west, so the S connectors do not meet.

Answer: D

A's port faces west, so the touching edge of B must face the opposite way, east, and that edge must carry D. B's D starts on its top (north) edge, and moving it north to east takes one clockwise quarter turn, so B must turn 90 degrees clockwise. Only that picture puts D on B's joining edge, against A's D.

• A: Turning B 180 degrees clockwise puts the letter M on the joining east edge and leaves D facing south, so the D connectors do not meet.
• B: Turning B 270 degrees clockwise puts the letter Q on the joining east edge and leaves D facing west, so the D connectors do not meet.
• C: Leaving B unturned puts the letter T on the joining east edge and leaves D facing north, so the D connectors do not meet.
• D (correct): A 90 degree clockwise turn carries D from B's north edge to its east edge, right against A's D port.

Answer: B

A's port faces east, so the touching edge of B must face the opposite way, west, and that edge must carry V. B's V starts on its bottom (south) edge, and moving it south to west takes one clockwise quarter turn, so B must turn 90 degrees clockwise. Only that picture puts V on B's joining edge, against A's V.

• A: Turning B 180 degrees clockwise puts the letter T on the joining west edge and leaves V facing north, so the V connectors do not meet.
• B (correct): A 90 degree clockwise turn carries V from B's south edge to its west edge, right against A's V port.
• C: Leaving B unturned puts the letter R on the joining west edge and leaves V facing south, so the V connectors do not meet.
• D: Turning B 270 degrees clockwise puts the letter W on the joining west edge and leaves V facing east, so the V connectors do not meet.

Answer: C

A's port faces north, so the touching edge of B must face the opposite way, south, and that edge must carry F. B's F starts on its right (east) edge, and moving it east to south takes one clockwise quarter turn, so B must turn 90 degrees clockwise. Only that picture puts F on B's joining edge, against A's F.

• A: Leaving B unturned puts the letter K on the joining south edge and leaves F facing east, so the F connectors do not meet.
• B: Turning B 270 degrees clockwise puts the letter N on the joining south edge and leaves F facing north, so the F connectors do not meet.
• C (correct): A 90 degree clockwise turn carries F from B's east edge to its south edge, right against A's F port.
• D: Turning B 180 degrees clockwise puts the letter Z on the joining south edge and leaves F facing west, so the F connectors do not meet.

Answer: B

A's port faces west, so the touching edge of B must face the opposite way, east, and that edge must carry J. B's J starts on its left (west) edge, and moving it west to north to east takes two clockwise quarter turns, so B must turn 180 degrees clockwise. Only that picture puts J on B's joining edge, against A's J.

• A: Turning B 270 degrees clockwise puts the letter P on the joining east edge and leaves J facing south, so the J connectors do not meet.
• B (correct): A 180 degree clockwise turn carries J from B's west edge to its east edge, right against A's J port.
• C: Turning B 90 degrees clockwise puts the letter C on the joining east edge and leaves J facing north, so the J connectors do not meet.
• D: Leaving B unturned puts the letter L on the joining east edge and leaves J facing west, so the J connectors do not meet.

Answer: B

A's port faces south, so the touching edge of B must face the opposite way, north, and that edge must carry B. B's B starts on its right (east) edge, and moving it east to south to west to north takes three clockwise quarter turns, so B must turn 270 degrees clockwise (the same as one quarter turn counterclockwise). Only that picture puts B on B's joining edge, against A's B.

• A: Leaving B unturned puts the letter G on the joining north edge and leaves B facing east, so the B connectors do not meet.
• B (correct): A 270 degree clockwise turn carries B from B's east edge to its north edge, right against A's B port.
• C: Turning B 180 degrees clockwise puts the letter D on the joining north edge and leaves B facing west, so the B connectors do not meet.
• D: Turning B 90 degrees clockwise puts the letter H on the joining north edge and leaves B facing south, so the B connectors do not meet.

Answer: A

A's port faces east, so the touching edge of B must face the opposite way, west, and that edge must carry U. B's U starts on its top (north) edge, and moving it north to east to south to west takes three clockwise quarter turns, so B must turn 270 degrees clockwise (the same as one quarter turn counterclockwise). Only that picture puts U on B's joining edge, against A's U.

• A (correct): A 270 degree clockwise turn carries U from B's north edge to its west edge, right against A's U port.
• B: Turning B 180 degrees clockwise puts the letter A on the joining west edge and leaves U facing south, so the U connectors do not meet.
• C: Leaving B unturned puts the letter R on the joining west edge and leaves U facing north, so the U connectors do not meet.
• D: Turning B 90 degrees clockwise puts the letter W on the joining west edge and leaves U facing east, so the U connectors do not meet.

Answer: D

A's port faces west, so the touching edge of B must face the opposite way, east, and that edge must carry Y. B's Y starts on its bottom (south) edge, and moving it south to west to north to east takes three clockwise quarter turns, so B must turn 270 degrees clockwise (the same as one quarter turn counterclockwise). Only that picture puts Y on B's joining edge, against A's Y.

• A: Turning B 90 degrees clockwise puts the letter P on the joining east edge and leaves Y facing west, so the Y connectors do not meet.
• B: Leaving B unturned puts the letter C on the joining east edge and leaves Y facing south, so the Y connectors do not meet.
• C: Turning B 180 degrees clockwise puts the letter G on the joining east edge and leaves Y facing north, so the Y connectors do not meet.
• D (correct): A 270 degree clockwise turn carries Y from B's south edge to its east edge, right against A's Y port.

Answer: B

A's port faces north, so the touching edge of B must face the opposite way, south, and that edge must carry T. B's T is already on its bottom (south) edge, so B needs no turn at all; it slides straight into place. Only that picture puts T on B's joining edge, against A's T.

• A: Turning B 270 degrees clockwise puts the letter J on the joining south edge and leaves T facing east, so the T connectors do not meet.
• B (correct): Left unturned, B already has T on its south edge, so it meets A's T port directly.
• C: Turning B 90 degrees clockwise puts the letter V on the joining south edge and leaves T facing west, so the T connectors do not meet.
• D: Turning B 180 degrees clockwise puts the letter Q on the joining south edge and leaves T facing north, so the T connectors do not meet.

Answer: A

A's port faces south, so the touching edge of B must face the opposite way, north, and that edge must carry N. B's N is already on its top (north) edge, so B needs no turn at all; it slides straight into place. Only that picture puts N on B's joining edge, against A's N.

• A (correct): Left unturned, B already has N on its north edge, so it meets A's N port directly.
• B: Turning B 270 degrees clockwise puts the letter R on the joining north edge and leaves N facing west, so the N connectors do not meet.
• C: Turning B 180 degrees clockwise puts the letter S on the joining north edge and leaves N facing south, so the N connectors do not meet.
• D: Turning B 90 degrees clockwise puts the letter M on the joining north edge and leaves N facing east, so the N connectors do not meet.

Answer: D

A's port faces east, so the touching edge of B must face the opposite way, west, and that edge must carry L. B's L starts on its right (east) edge, and moving it east to south to west takes two clockwise quarter turns, so B must turn 180 degrees clockwise. Only that picture puts L on B's joining edge, against A's L.

• A: Turning B 90 degrees clockwise puts the letter C on the joining west edge and leaves L facing south, so the L connectors do not meet.
• B: Leaving B unturned puts the letter H on the joining west edge and leaves L facing east, so the L connectors do not meet.
• C: Turning B 270 degrees clockwise puts the letter P on the joining west edge and leaves L facing north, so the L connectors do not meet.
• D (correct): A 180 degree clockwise turn carries L from B's east edge to its west edge, right against A's L port.

Answer: B

A's port faces west, so the touching edge of B must face the opposite way, east, and that edge must carry W. B's W starts on its top (north) edge, and moving it north to east takes one clockwise quarter turn, so B must turn 90 degrees clockwise. Only that picture puts W on B's joining edge, against A's W.

• A: Turning B 270 degrees clockwise puts the letter E on the joining east edge and leaves W facing west, so the W connectors do not meet.
• B (correct): A 90 degree clockwise turn carries W from B's north edge to its east edge, right against A's W port.
• C: Leaving B unturned puts the letter S on the joining east edge and leaves W facing north, so the W connectors do not meet.
• D: Turning B 180 degrees clockwise puts the letter K on the joining east edge and leaves W facing south, so the W connectors do not meet.

Answer: C

A's port faces north, so the touching edge of B must face the opposite way, south, and that edge must carry C. B's C starts on its right (east) edge, and moving it east to south takes one clockwise quarter turn, so B must turn 90 degrees clockwise. Only that picture puts C on B's joining edge, against A's C.

• A: Turning B 270 degrees clockwise puts the letter S on the joining south edge and leaves C facing north, so the C connectors do not meet.
• B: Turning B 180 degrees clockwise puts the letter R on the joining south edge and leaves C facing west, so the C connectors do not meet.
• C (correct): A 90 degree clockwise turn carries C from B's east edge to its south edge, right against A's C port.
• D: Leaving B unturned puts the letter H on the joining south edge and leaves C facing east, so the C connectors do not meet.

Answer: A

A's port faces south, so the touching edge of B must face the opposite way, north, and that edge must carry M. B's M starts on its right (east) edge, and moving it east to south to west to north takes three clockwise quarter turns, so B must turn 270 degrees clockwise (the same as one quarter turn counterclockwise). Only that picture puts M on B's joining edge, against A's M.

• A (correct): A 270 degree clockwise turn carries M from B's east edge to its north edge, right against A's M port.
• B: Leaving B unturned puts the letter F on the joining north edge and leaves M facing east, so the M connectors do not meet.
• C: Turning B 180 degrees clockwise puts the letter N on the joining north edge and leaves M facing west, so the M connectors do not meet.
• D: Turning B 90 degrees clockwise puts the letter L on the joining north edge and leaves M facing south, so the M connectors do not meet.

Answer: D

Check one letter at a time. Point R is at the middle of a long side of the rectangle, and point S is at a corner of the long side of the trapezoid. Cross out any figure where either end of the line lands somewhere else or where a shape has changed. The shapes may be turned, so find each point by its place on the shape (corner, middle of a side, center), not by up, down, left or right.

• A: The line ends in the wrong place: it meets the trapezoid at the middle of a slanted side, but point S is at a corner of the long side.
• B: The line ends in the wrong place: it meets the rectangle at a corner, but point R is at the middle of a long side.
• C: The line ends in the wrong place: it meets the rectangle at the center, but point R is at the middle of a long side and it meets the trapezoid at the middle of a slanted side, but point S is at a corner of the long side.
• D (correct): The line joins the middle of a long side of the rectangle to a corner of the long side of the trapezoid, the same spots as points R and S in the left box; turning a shape does not move a point on it.

Answer: D

Check one letter at a time. Point E is at the middle of a long side of the rectangle, and point F is at the middle of a wall of the house shape. Cross out any figure where either end of the line lands somewhere else or where a shape has changed. The shapes may be turned, so find each point by its place on the shape (corner, middle of a side, center), not by up, down, left or right.

• A: The line ends in the wrong place: it meets the rectangle at a corner, but point E is at the middle of a long side.
• B: The line ends in the wrong place: it meets the rectangle at the middle of a short side, but point E is at the middle of a long side.
• C: One of the shapes here is a parallelogram, but the left box has a rectangle. Joining parts never changes a shape.
• D (correct): The line joins the middle of a long side of the rectangle to the middle of a wall of the house shape, the same spots as points E and F in the left box; turning a shape does not move a point on it.

Answer: C

Check one letter at a time. Point T is at the middle of a slanted side of the trapezoid, and point U is at the middle of a side of the triangle. Cross out any figure where either end of the line lands somewhere else or where a shape has changed. The shapes may be turned, so find each point by its place on the shape (corner, middle of a side, center), not by up, down, left or right.

• A: The line ends in the wrong place: it meets the trapezoid at a corner of the long side, but point T is at the middle of a slanted side and it meets the triangle at a corner, but point U is at the middle of a side.
• B: The line ends in the wrong place: it meets the trapezoid at the middle of the short side, but point T is at the middle of a slanted side.
• C (correct): The line joins the middle of a slanted side of the trapezoid to the middle of a side of the triangle, the same spots as points T and U in the left box; turning a shape does not move a point on it.
• D: The line ends in the wrong place: it meets the triangle at the center, but point U is at the middle of a side.

Answer: A

Check one letter at a time. Point M is at the sharpest corner of the right triangle, and point N is at a corner of the flat side of the half-circle. Cross out any figure where either end of the line lands somewhere else or where a shape has changed. The shapes may be turned, so find each point by its place on the shape (corner, middle of a side, center), not by up, down, left or right.

• A (correct): The line joins the sharpest corner of the right triangle to a corner of the flat side of the half-circle, the same spots as points M and N in the left box; turning a shape does not move a point on it.
• B: The line ends in the wrong place: it meets the half-circle at the top of the curved side, but point N is at a corner of the flat side.
• C: The line ends in the wrong place: it meets the right triangle at the middle of the longer leg, but point M is at the sharpest corner.
• D: The line ends in the wrong place: it meets the right triangle at the middle of the shorter leg, but point M is at the sharpest corner.

Answer: B

Check one letter at a time. Point G is at a corner of the triangle, and point H is at a sharp corner of the parallelogram. Cross out any figure where either end of the line lands somewhere else or where a shape has changed. The shapes may be turned, so find each point by its place on the shape (corner, middle of a side, center), not by up, down, left or right.

• A: The line ends in the wrong place: it meets the triangle at the middle of a side, but point G is at a corner and it meets the parallelogram at the middle of a short side, but point H is at a sharp corner.
• B (correct): The line joins a corner of the triangle to a sharp corner of the parallelogram, the same spots as points G and H in the left box; turning a shape does not move a point on it.
• C: The line ends in the wrong place: it meets the parallelogram at the middle of a long side, but point H is at a sharp corner.
• D: The line ends in the wrong place: it meets the parallelogram at the middle of a short side, but point H is at a sharp corner.

Answer: D

Check one letter at a time. Point M is at the middle of the slanted side of the right triangle, and point N is at the middle of a slanted side of the trapezoid. Cross out any figure where either end of the line lands somewhere else or where a shape has changed. The shapes may be turned, so find each point by its place on the shape (corner, middle of a side, center), not by up, down, left or right.

• A: The line ends in the wrong place: it meets the trapezoid at the middle of the long side, but point N is at the middle of a slanted side.
• B: The line ends in the wrong place: it meets the right triangle at the middle of the longer leg, but point M is at the middle of the slanted side and it meets the trapezoid at a corner of the long side, but point N is at the middle of a slanted side.
• C: The line ends in the wrong place: it meets the trapezoid at a corner of the long side, but point N is at the middle of a slanted side.
• D (correct): The line joins the middle of the slanted side of the right triangle to the middle of a slanted side of the trapezoid, the same spots as points M and N in the left box; turning a shape does not move a point on it.

Answer: D

Check one letter at a time. Point G is at the top of the curved side of the half-circle, and point H is at a corner of the hexagon. Cross out any figure where either end of the line lands somewhere else or where a shape has changed. The shapes may be turned, so find each point by its place on the shape (corner, middle of a side, center), not by up, down, left or right.

• A: The line ends in the wrong place: it meets the hexagon at the middle of a side, but point H is at a corner.
• B: The line ends in the wrong place: it meets the half-circle at a corner of the flat side, but point G is at the top of the curved side.
• C: The line ends in the wrong place: it meets the half-circle at a corner of the flat side, but point G is at the top of the curved side and it meets the hexagon at the middle of a side, but point H is at a corner.
• D (correct): The line joins the top of the curved side of the half-circle to a corner of the hexagon, the same spots as points G and H in the left box; turning a shape does not move a point on it.

Answer: C

Check one letter at a time. Point P is at the center of the rectangle, and point Q is at the middle of the longer leg of the right triangle. Cross out any figure where either end of the line lands somewhere else or where a shape has changed. The shapes may be turned, so find each point by its place on the shape (corner, middle of a side, center), not by up, down, left or right.

• A: The line ends in the wrong place: it meets the right triangle at the sharpest corner, but point Q is at the middle of the longer leg.
• B: One of the shapes here is a parallelogram, but the left box has a rectangle. Joining parts never changes a shape.
• C (correct): The line joins the center of the rectangle to the middle of the longer leg of the right triangle, the same spots as points P and Q in the left box; turning a shape does not move a point on it.
• D: The line ends in the wrong place: it meets the right triangle at the middle of the slanted side, but point Q is at the middle of the longer leg.

Answer: A

Check one letter at a time. Point X is at the center of the triangle, and point Y is at the middle of a long side of the rectangle. Cross out any figure where either end of the line lands somewhere else or where a shape has changed. The shapes may be turned, so find each point by its place on the shape (corner, middle of a side, center), not by up, down, left or right.

• A (correct): The line joins the center of the triangle to the middle of a long side of the rectangle, the same spots as points X and Y in the left box; turning a shape does not move a point on it.
• B: The line ends in the wrong place: it meets the triangle at the middle of a side, but point X is at the center.
• C: The line ends in the wrong place: it meets the triangle at the middle of a side, but point X is at the center and it meets the rectangle at the middle of a short side, but point Y is at the middle of a long side.
• D: The line ends in the wrong place: it meets the rectangle at the center, but point Y is at the middle of a long side.

Answer: C

Check one letter at a time. Point V is at a corner where the roof meets a wall of the house shape, and point W is at the sharpest corner of the right triangle. Cross out any figure where either end of the line lands somewhere else or where a shape has changed. The shapes may be turned, so find each point by its place on the shape (corner, middle of a side, center), not by up, down, left or right.

• A: The line ends in the wrong place: it meets the right triangle at the middle of the slanted side, but point W is at the sharpest corner.
• B: The line ends in the wrong place: it meets the house shape at the middle of a wall, but point V is at a corner where the roof meets a wall.
• C (correct): The line joins a corner where the roof meets a wall of the house shape to the sharpest corner of the right triangle, the same spots as points V and W in the left box; turning a shape does not move a point on it.
• D: The line ends in the wrong place: it meets the house shape at the middle of the bottom side, but point V is at a corner where the roof meets a wall and it meets the right triangle at the middle of the slanted side, but point W is at the sharpest corner.

Answer: A

Check one letter at a time. Point R is at a corner of the short side of the trapezoid, and point S is at the center of the rectangle. Cross out any figure where either end of the line lands somewhere else or where a shape has changed. The shapes may be turned, so find each point by its place on the shape (corner, middle of a side, center), not by up, down, left or right.

• A (correct): The line joins a corner of the short side of the trapezoid to the center of the rectangle, the same spots as points R and S in the left box; turning a shape does not move a point on it.
• B: The line ends in the wrong place: it meets the trapezoid at a corner of the long side, but point R is at a corner of the short side.
• C: One of the shapes here is a square, but the left box has a rectangle. Joining parts never changes a shape.
• D: The line ends in the wrong place: it meets the rectangle at a corner, but point S is at the center.

Answer: B

Check one letter at a time. Point J is at the middle of a side of the diamond, and point K is at the middle of a side of the square. Cross out any figure where either end of the line lands somewhere else or where a shape has changed. The shapes may be turned, so find each point by its place on the shape (corner, middle of a side, center), not by up, down, left or right.

• A: The line ends in the wrong place: it meets the diamond at a wide corner, but point J is at the middle of a side and it meets the square at a corner, but point K is at the middle of a side.
• B (correct): The line joins the middle of a side of the diamond to the middle of a side of the square, the same spots as points J and K in the left box; turning a shape does not move a point on it.
• C: The line ends in the wrong place: it meets the diamond at a wide corner, but point J is at the middle of a side.
• D: The line ends in the wrong place: it meets the square at the center, but point K is at the middle of a side.

Answer: B

Check one letter at a time. Point V is at a corner of the pentagon, and point W is at a corner of the long side of the trapezoid. Cross out any figure where either end of the line lands somewhere else or where a shape has changed. The shapes may be turned, so find each point by its place on the shape (corner, middle of a side, center), not by up, down, left or right.

• A: The line ends in the wrong place: it meets the pentagon at the middle of a side, but point V is at a corner and it meets the trapezoid at the middle of the long side, but point W is at a corner of the long side.
• B (correct): The line joins a corner of the pentagon to a corner of the long side of the trapezoid, the same spots as points V and W in the left box; turning a shape does not move a point on it.
• C: The line ends in the wrong place: it meets the trapezoid at the middle of a slanted side, but point W is at a corner of the long side.
• D: The line ends in the wrong place: it meets the pentagon at the center, but point V is at a corner.

Answer: C

Check one letter at a time. Point J is at the top of the curved side of the half-circle, and point K is at a corner of the short side of the trapezoid. Cross out any figure where either end of the line lands somewhere else or where a shape has changed. The shapes may be turned, so find each point by its place on the shape (corner, middle of a side, center), not by up, down, left or right.

• A: The line ends in the wrong place: it meets the half-circle at a corner of the flat side, but point J is at the top of the curved side and it meets the trapezoid at the middle of the short side, but point K is at a corner of the short side.
• B: The line ends in the wrong place: it meets the trapezoid at a corner of the long side, but point K is at a corner of the short side.
• C (correct): The line joins the top of the curved side of the half-circle to a corner of the short side of the trapezoid, the same spots as points J and K in the left box; turning a shape does not move a point on it.
• D: The line ends in the wrong place: it meets the half-circle at the middle of the flat side, but point J is at the top of the curved side.

Answer: B

Check one letter at a time. Point M is at the center of the pentagon, and point N is at the middle of a long side of the parallelogram. Cross out any figure where either end of the line lands somewhere else or where a shape has changed. The shapes may be turned, so find each point by its place on the shape (corner, middle of a side, center), not by up, down, left or right.

• A: One of the shapes here is a rectangle, but the left box has a parallelogram. Joining parts never changes a shape.
• B (correct): The line joins the center of the pentagon to the middle of a long side of the parallelogram, the same spots as points M and N in the left box; turning a shape does not move a point on it.
• C: The line ends in the wrong place: it meets the parallelogram at the center, but point N is at the middle of a long side.
• D: The line ends in the wrong place: it meets the parallelogram at a wide corner, but point N is at the middle of a long side.

Answer: D

Check one letter at a time. Point E is at the middle of a short side of the rectangle, and point F is at a corner of the hexagon. Cross out any figure where either end of the line lands somewhere else or where a shape has changed. The shapes may be turned, so find each point by its place on the shape (corner, middle of a side, center), not by up, down, left or right.

• A: The line ends in the wrong place: it meets the hexagon at the middle of a side, but point F is at a corner.
• B: The line ends in the wrong place: it meets the rectangle at the middle of a long side, but point E is at the middle of a short side.
• C: One of the shapes here is a parallelogram, but the left box has a rectangle. Joining parts never changes a shape.
• D (correct): The line joins the middle of a short side of the rectangle to a corner of the hexagon, the same spots as points E and F in the left box; turning a shape does not move a point on it.

Answer: C

Check one letter at a time. Point M is at the middle of the bottom side of the house shape, and point N is at the center of the pentagon. Cross out any figure where either end of the line lands somewhere else or where a shape has changed. The shapes may be turned, so find each point by its place on the shape (corner, middle of a side, center), not by up, down, left or right.

• A: The line ends in the wrong place: it meets the house shape at the peak of the roof, but point M is at the middle of the bottom side.
• B: The line ends in the wrong place: it meets the house shape at a corner where the roof meets a wall, but point M is at the middle of the bottom side and it meets the pentagon at a corner, but point N is at the center.
• C (correct): The line joins the middle of the bottom side of the house shape to the center of the pentagon, the same spots as points M and N in the left box; turning a shape does not move a point on it.
• D: The line ends in the wrong place: it meets the pentagon at the middle of a side, but point N is at the center.

Answer: B

Check one letter at a time. Point V is at the center of the triangle, and point W is at a sharp corner of the parallelogram. Cross out any figure where either end of the line lands somewhere else or where a shape has changed. The shapes may be turned, so find each point by its place on the shape (corner, middle of a side, center), not by up, down, left or right.

• A: The line ends in the wrong place: it meets the parallelogram at the middle of a long side, but point W is at a sharp corner.
• B (correct): The line joins the center of the triangle to a sharp corner of the parallelogram, the same spots as points V and W in the left box; turning a shape does not move a point on it.
• C: The line ends in the wrong place: it meets the triangle at a corner, but point V is at the center and it meets the parallelogram at the center, but point W is at a sharp corner.
• D: The line ends in the wrong place: it meets the parallelogram at the center, but point W is at a sharp corner.

Answer: C

Check one letter at a time. Point E is at a corner of the flat side of the half-circle, and point F is at the middle of the shorter leg of the right triangle. Cross out any figure where either end of the line lands somewhere else or where a shape has changed. The shapes may be turned, so find each point by its place on the shape (corner, middle of a side, center), not by up, down, left or right.

• A: The line ends in the wrong place: it meets the half-circle at the top of the curved side, but point E is at a corner of the flat side.
• B: The line ends in the wrong place: it meets the right triangle at the middle of the longer leg, but point F is at the middle of the shorter leg.
• C (correct): The line joins a corner of the flat side of the half-circle to the middle of the shorter leg of the right triangle, the same spots as points E and F in the left box; turning a shape does not move a point on it.
• D: The line ends in the wrong place: it meets the half-circle at the middle of the flat side, but point E is at a corner of the flat side and it meets the right triangle at the middle of the slanted side, but point F is at the middle of the shorter leg.

Answer: C

Check one letter at a time. Point E is at a corner of the pentagon, and point F is at a corner of the rectangle. Cross out any figure where either end of the line lands somewhere else or where a shape has changed. The shapes may be turned, so find each point by its place on the shape (corner, middle of a side, center), not by up, down, left or right.

• A: The line ends in the wrong place: it meets the rectangle at the middle of a short side, but point F is at a corner.
• B: One of the shapes here is a square, but the left box has a rectangle. Joining parts never changes a shape.
• C (correct): The line joins a corner of the pentagon to a corner of the rectangle, the same spots as points E and F in the left box; turning a shape does not move a point on it.
• D: The line ends in the wrong place: it meets the pentagon at the center, but point E is at a corner.

Answer: A

Check one letter at a time. Point G is at the middle of a side of the triangle, and point H is at the middle of a long side of the rectangle. Cross out any figure where either end of the line lands somewhere else or where a shape has changed. The shapes may be turned, so find each point by its place on the shape (corner, middle of a side, center), not by up, down, left or right.

• A (correct): The line joins the middle of a side of the triangle to the middle of a long side of the rectangle, the same spots as points G and H in the left box; turning a shape does not move a point on it.
• B: The line ends in the wrong place: it meets the triangle at the center, but point G is at the middle of a side.
• C: One of the shapes here is a parallelogram, but the left box has a rectangle. Joining parts never changes a shape.
• D: The line ends in the wrong place: it meets the rectangle at the center, but point H is at the middle of a long side.

Answer: B

Check one letter at a time. Point V is at the middle of a side of the pentagon, and point W is at the middle of the long side of the trapezoid. Cross out any figure where either end of the line lands somewhere else or where a shape has changed. The shapes may be turned, so find each point by its place on the shape (corner, middle of a side, center), not by up, down, left or right.

• A: One of the shapes here is a hexagon, but the left box has a pentagon. Joining parts never changes a shape.
• B (correct): The line joins the middle of a side of the pentagon to the middle of the long side of the trapezoid, the same spots as points V and W in the left box; turning a shape does not move a point on it.
• C: The line ends in the wrong place: it meets the trapezoid at the middle of a slanted side, but point W is at the middle of the long side.
• D: The line ends in the wrong place: it meets the trapezoid at a corner of the short side, but point W is at the middle of the long side.

Answer: A

Check one letter at a time. Point T is at a corner of the triangle, and point U is at the center of the square. Cross out any figure where either end of the line lands somewhere else or where a shape has changed. The shapes may be turned, so find each point by its place on the shape (corner, middle of a side, center), not by up, down, left or right.

• A (correct): The line joins a corner of the triangle to the center of the square, the same spots as points T and U in the left box; turning a shape does not move a point on it.
• B: The line ends in the wrong place: it meets the square at the middle of a side, but point U is at the center.
• C: The line ends in the wrong place: it meets the triangle at the middle of a side, but point T is at a corner.
• D: One of the shapes here is a rectangle, but the left box has a square. Joining parts never changes a shape.

Answer: C

Check one letter at a time. Point J is at a sharp corner of the parallelogram, and point K is at the middle of a short side of the rectangle. Cross out any figure where either end of the line lands somewhere else or where a shape has changed. The shapes may be turned, so find each point by its place on the shape (corner, middle of a side, center), not by up, down, left or right.

• A: The line ends in the wrong place: it meets the parallelogram at the middle of a short side, but point J is at a sharp corner.
• B: The line ends in the wrong place: it meets the parallelogram at the middle of a long side, but point J is at a sharp corner and it meets the rectangle at the middle of a long side, but point K is at the middle of a short side.
• C (correct): The line joins a sharp corner of the parallelogram to the middle of a short side of the rectangle, the same spots as points J and K in the left box; turning a shape does not move a point on it.
• D: The line ends in the wrong place: it meets the parallelogram at a wide corner, but point J is at a sharp corner.

Answer: A

Check one letter at a time. Point T is at a sharp corner of the diamond, and point U is at a corner of the short side of the trapezoid. Cross out any figure where either end of the line lands somewhere else or where a shape has changed. The shapes may be turned, so find each point by its place on the shape (corner, middle of a side, center), not by up, down, left or right.

• A (correct): The line joins a sharp corner of the diamond to a corner of the short side of the trapezoid, the same spots as points T and U in the left box; turning a shape does not move a point on it.
• B: The line ends in the wrong place: it meets the trapezoid at the middle of the short side, but point U is at a corner of the short side.
• C: The line ends in the wrong place: it meets the diamond at the middle of a side, but point T is at a sharp corner.
• D: The line ends in the wrong place: it meets the diamond at a wide corner, but point T is at a sharp corner and it meets the trapezoid at the middle of the long side, but point U is at a corner of the short side.

Answer: C

Check one letter at a time. Point J is at the middle of a side of the hexagon, and point K is at the middle of a short side of the parallelogram. Cross out any figure where either end of the line lands somewhere else or where a shape has changed. The shapes may be turned, so find each point by its place on the shape (corner, middle of a side, center), not by up, down, left or right.

• A: The line ends in the wrong place: it meets the hexagon at a corner, but point J is at the middle of a side.
• B: The line ends in the wrong place: it meets the parallelogram at a sharp corner, but point K is at the middle of a short side.
• C (correct): The line joins the middle of a side of the hexagon to the middle of a short side of the parallelogram, the same spots as points J and K in the left box; turning a shape does not move a point on it.
• D: One of the shapes here is a pentagon, but the left box has a hexagon. Joining parts never changes a shape.

Answer: A

Check one letter at a time. Point K is at the center of the pentagon, and point L is at a corner where the roof meets a wall of the house shape. Cross out any figure where either end of the line lands somewhere else or where a shape has changed. The shapes may be turned, so find each point by its place on the shape (corner, middle of a side, center), not by up, down, left or right.

• A (correct): The line joins the center of the pentagon to a corner where the roof meets a wall of the house shape, the same spots as points K and L in the left box; turning a shape does not move a point on it.
• B: The line ends in the wrong place: it meets the house shape at the peak of the roof, but point L is at a corner where the roof meets a wall.
• C: The line ends in the wrong place: it meets the pentagon at a corner, but point K is at the center.
• D: One of the shapes here is a hexagon, but the left box has a pentagon. Joining parts never changes a shape.

Answer: B

Check one letter at a time. Point E is at a corner of the pentagon, and point F is at a corner of the hexagon. Cross out any figure where either end of the line lands somewhere else or where a shape has changed. The shapes may be turned, so find each point by its place on the shape (corner, middle of a side, center), not by up, down, left or right.

• A: The line ends in the wrong place: it meets the pentagon at the center, but point E is at a corner and it meets the hexagon at the middle of a side, but point F is at a corner.
• B (correct): The line joins a corner of the pentagon to a corner of the hexagon, the same spots as points E and F in the left box; turning a shape does not move a point on it.
• C: The line ends in the wrong place: it meets the pentagon at the center, but point E is at a corner.
• D: The line ends in the wrong place: it meets the pentagon at the middle of a side, but point E is at a corner.

Answer: C

Check one letter at a time. Point E is at the center of the rectangle, and point F is at the middle of a side of the triangle. Cross out any figure where either end of the line lands somewhere else or where a shape has changed. The shapes may be turned, so find each point by its place on the shape (corner, middle of a side, center), not by up, down, left or right.

• A: The line ends in the wrong place: it meets the rectangle at the middle of a short side, but point E is at the center.
• B: One of the shapes here is a square, but the left box has a rectangle. Joining parts never changes a shape.
• C (correct): The line joins the center of the rectangle to the middle of a side of the triangle, the same spots as points E and F in the left box; turning a shape does not move a point on it.
• D: The line ends in the wrong place: it meets the triangle at a corner, but point F is at the middle of a side.

Answer: B

Check one letter at a time. Point V is at a corner where the roof meets a wall of the house shape, and point W is at the middle of a side of the square. Cross out any figure where either end of the line lands somewhere else or where a shape has changed. The shapes may be turned, so find each point by its place on the shape (corner, middle of a side, center), not by up, down, left or right.

• A: The line ends in the wrong place: it meets the house shape at the peak of the roof, but point V is at a corner where the roof meets a wall.
• B (correct): The line joins a corner where the roof meets a wall of the house shape to the middle of a side of the square, the same spots as points V and W in the left box; turning a shape does not move a point on it.
• C: One of the shapes here is a diamond, but the left box has a square. Joining parts never changes a shape.
• D: The line ends in the wrong place: it meets the house shape at the middle of a wall, but point V is at a corner where the roof meets a wall.

Answer: B

Check one letter at a time. Point J is at the middle of a side of the triangle, and point K is at the center of the parallelogram. Cross out any figure where either end of the line lands somewhere else or where a shape has changed. The shapes may be turned, so find each point by its place on the shape (corner, middle of a side, center), not by up, down, left or right.

• A: The line ends in the wrong place: it meets the parallelogram at a sharp corner, but point K is at the center.
• B (correct): The line joins the middle of a side of the triangle to the center of the parallelogram, the same spots as points J and K in the left box; turning a shape does not move a point on it.
• C: The line ends in the wrong place: it meets the parallelogram at the middle of a short side, but point K is at the center.
• D: One of the shapes here is a rectangle, but the left box has a parallelogram. Joining parts never changes a shape.

Answer: D

Check one letter at a time. Point T is at the center of the square, and point U is at a corner of the rectangle. Cross out any figure where either end of the line lands somewhere else or where a shape has changed. The shapes may be turned, so find each point by its place on the shape (corner, middle of a side, center), not by up, down, left or right.

• A: One of the shapes here is a diamond, but the left box has a square. Joining parts never changes a shape.
• B: The line ends in the wrong place: it meets the rectangle at the center, but point U is at a corner.
• C: The line ends in the wrong place: it meets the square at a corner, but point T is at the center.
• D (correct): The line joins the center of the square to a corner of the rectangle, the same spots as points T and U in the left box; turning a shape does not move a point on it.

Answer: C

Check one letter at a time. Point E is at the middle of the shorter leg of the right triangle, and point F is at the middle of a short side of the parallelogram. Cross out any figure where either end of the line lands somewhere else or where a shape has changed. The shapes may be turned, so find each point by its place on the shape (corner, middle of a side, center), not by up, down, left or right.

• A: The line ends in the wrong place: it meets the right triangle at the sharpest corner, but point E is at the middle of the shorter leg.
• B: The line ends in the wrong place: it meets the parallelogram at the middle of a long side, but point F is at the middle of a short side.
• C (correct): The line joins the middle of the shorter leg of the right triangle to the middle of a short side of the parallelogram, the same spots as points E and F in the left box; turning a shape does not move a point on it.
• D: One of the shapes here is a rectangle, but the left box has a parallelogram. Joining parts never changes a shape.

Answer: C

Check one letter at a time. Point J is at a corner of the rectangle, and point K is at the middle of the slanted side of the right triangle. Cross out any figure where either end of the line lands somewhere else or where a shape has changed. The shapes may be turned, so find each point by its place on the shape (corner, middle of a side, center), not by up, down, left or right.

• A: The line ends in the wrong place: it meets the right triangle at the middle of the longer leg, but point K is at the middle of the slanted side.
• B: One of the shapes here is a square, but the left box has a rectangle. Joining parts never changes a shape.
• C (correct): The line joins a corner of the rectangle to the middle of the slanted side of the right triangle, the same spots as points J and K in the left box; turning a shape does not move a point on it.
• D: The line ends in the wrong place: it meets the right triangle at the middle of the shorter leg, but point K is at the middle of the slanted side.

Answer: A

Check one letter at a time. Point M is at the center of the triangle, and point N is at the top of the curved side of the half-circle. Cross out any figure where either end of the line lands somewhere else or where a shape has changed. The shapes may be turned, so find each point by its place on the shape (corner, middle of a side, center), not by up, down, left or right.

• A (correct): The line joins the center of the triangle to the top of the curved side of the half-circle, the same spots as points M and N in the left box; turning a shape does not move a point on it.
• B: The line ends in the wrong place: it meets the triangle at the middle of a side, but point M is at the center.
• C: The line ends in the wrong place: it meets the half-circle at a corner of the flat side, but point N is at the top of the curved side.
• D: The line ends in the wrong place: it meets the triangle at the middle of a side, but point M is at the center and it meets the half-circle at a corner of the flat side, but point N is at the top of the curved side.

Answer: D

Check one letter at a time. Point G is at a corner of the pentagon, and point H is at the center of the rectangle. Cross out any figure where either end of the line lands somewhere else or where a shape has changed. The shapes may be turned, so find each point by its place on the shape (corner, middle of a side, center), not by up, down, left or right.

• A: The line ends in the wrong place: it meets the pentagon at the center, but point G is at a corner.
• B: The line ends in the wrong place: it meets the rectangle at the middle of a long side, but point H is at the center.
• C: One of the shapes here is a parallelogram, but the left box has a rectangle. Joining parts never changes a shape.
• D (correct): The line joins a corner of the pentagon to the center of the rectangle, the same spots as points G and H in the left box; turning a shape does not move a point on it.

Answer: B

Check one letter at a time. Point X is at a corner of the rectangle, and point Y is at a corner of the flat side of the half-circle. Cross out any figure where either end of the line lands somewhere else or where a shape has changed. The shapes may be turned, so find each point by its place on the shape (corner, middle of a side, center), not by up, down, left or right.

• A: The line ends in the wrong place: it meets the rectangle at the center, but point X is at a corner.
• B (correct): The line joins a corner of the rectangle to a corner of the flat side of the half-circle, the same spots as points X and Y in the left box; turning a shape does not move a point on it.
• C: The line ends in the wrong place: it meets the rectangle at the middle of a long side, but point X is at a corner.
• D: The line ends in the wrong place: it meets the rectangle at the center, but point X is at a corner and it meets the half-circle at the top of the curved side, but point Y is at a corner of the flat side.

Answer: C

Check one letter at a time. Point K is at a bottom corner of the house shape, and point L is at the center of the triangle. Cross out any figure where either end of the line lands somewhere else or where a shape has changed. The shapes may be turned, so find each point by its place on the shape (corner, middle of a side, center), not by up, down, left or right.

• A: The line ends in the wrong place: it meets the house shape at a corner where the roof meets a wall, but point K is at a bottom corner.
• B: The line ends in the wrong place: it meets the house shape at the middle of a wall, but point K is at a bottom corner.
• C (correct): The line joins a bottom corner of the house shape to the center of the triangle, the same spots as points K and L in the left box; turning a shape does not move a point on it.
• D: The line ends in the wrong place: it meets the house shape at the middle of a wall, but point K is at a bottom corner and it meets the triangle at the middle of a side, but point L is at the center.

Answer: C

Check one letter at a time. Point M is at the peak of the roof of the house shape, and point N is at the center of the hexagon. Cross out any figure where either end of the line lands somewhere else or where a shape has changed. The shapes may be turned, so find each point by its place on the shape (corner, middle of a side, center), not by up, down, left or right.

• A: The line ends in the wrong place: it meets the house shape at the middle of a wall, but point M is at the peak of the roof.
• B: The line ends in the wrong place: it meets the house shape at a corner where the roof meets a wall, but point M is at the peak of the roof.
• C (correct): The line joins the peak of the roof of the house shape to the center of the hexagon, the same spots as points M and N in the left box; turning a shape does not move a point on it.
• D: One of the shapes here is a pentagon, but the left box has a hexagon. Joining parts never changes a shape.

Answer: D

Check one letter at a time. Point V is at the center of the rectangle, and point W is at the middle of a wall of the house shape. Cross out any figure where either end of the line lands somewhere else or where a shape has changed. The shapes may be turned, so find each point by its place on the shape (corner, middle of a side, center), not by up, down, left or right.

• A: The line ends in the wrong place: it meets the rectangle at the middle of a long side, but point V is at the center.
• B: The line ends in the wrong place: it meets the house shape at a corner where the roof meets a wall, but point W is at the middle of a wall.
• C: The line ends in the wrong place: it meets the rectangle at a corner, but point V is at the center and it meets the house shape at the peak of the roof, but point W is at the middle of a wall.
• D (correct): The line joins the center of the rectangle to the middle of a wall of the house shape, the same spots as points V and W in the left box; turning a shape does not move a point on it.

Answer: C

Check one letter at a time. Point V is at a corner of the hexagon, and point W is at the middle of a side of the triangle. Cross out any figure where either end of the line lands somewhere else or where a shape has changed. The shapes may be turned, so find each point by its place on the shape (corner, middle of a side, center), not by up, down, left or right.

• A: The line ends in the wrong place: it meets the hexagon at the center, but point V is at a corner.
• B: One of the shapes here is a pentagon, but the left box has a hexagon. Joining parts never changes a shape.
• C (correct): The line joins a corner of the hexagon to the middle of a side of the triangle, the same spots as points V and W in the left box; turning a shape does not move a point on it.
• D: The line ends in the wrong place: it meets the hexagon at the middle of a side, but point V is at a corner.

Answer: B

Check one letter at a time. Point X is at a wide corner of the diamond, and point Y is at a corner of the long side of the trapezoid. Cross out any figure where either end of the line lands somewhere else or where a shape has changed. The shapes may be turned, so find each point by its place on the shape (corner, middle of a side, center), not by up, down, left or right.

• A: The line ends in the wrong place: it meets the diamond at the middle of a side, but point X is at a wide corner and it meets the trapezoid at the middle of the long side, but point Y is at a corner of the long side.
• B (correct): The line joins a wide corner of the diamond to a corner of the long side of the trapezoid, the same spots as points X and Y in the left box; turning a shape does not move a point on it.
• C: The line ends in the wrong place: it meets the diamond at the center, but point X is at a wide corner.
• D: The line ends in the wrong place: it meets the trapezoid at the middle of the short side, but point Y is at a corner of the long side.

Answer: C

Check one letter at a time. Point J is at the middle of the bottom side of the house shape, and point K is at a wide corner of the parallelogram. Cross out any figure where either end of the line lands somewhere else or where a shape has changed. The shapes may be turned, so find each point by its place on the shape (corner, middle of a side, center), not by up, down, left or right.

• A: The line ends in the wrong place: it meets the parallelogram at the middle of a short side, but point K is at a wide corner.
• B: The line ends in the wrong place: it meets the house shape at a corner where the roof meets a wall, but point J is at the middle of the bottom side.
• C (correct): The line joins the middle of the bottom side of the house shape to a wide corner of the parallelogram, the same spots as points J and K in the left box; turning a shape does not move a point on it.
• D: The line ends in the wrong place: it meets the house shape at the peak of the roof, but point J is at the middle of the bottom side.

Answer: A

Check one letter at a time. Point E is at the middle of a side of the diamond, and point F is at the middle of a long side of the parallelogram. Cross out any figure where either end of the line lands somewhere else or where a shape has changed. The shapes may be turned, so find each point by its place on the shape (corner, middle of a side, center), not by up, down, left or right.

• A (correct): The line joins the middle of a side of the diamond to the middle of a long side of the parallelogram, the same spots as points E and F in the left box; turning a shape does not move a point on it.
• B: One of the shapes here is a rectangle, but the left box has a parallelogram. Joining parts never changes a shape.
• C: The line ends in the wrong place: it meets the parallelogram at a sharp corner, but point F is at the middle of a long side.
• D: The line ends in the wrong place: it meets the parallelogram at a wide corner, but point F is at the middle of a long side.

Answer: B

Check one letter at a time. Point M is at the middle of the flat side of the half-circle, and point N is at the middle of a side of the hexagon. Cross out any figure where either end of the line lands somewhere else or where a shape has changed. The shapes may be turned, so find each point by its place on the shape (corner, middle of a side, center), not by up, down, left or right.

• A: One of the shapes here is a pentagon, but the left box has a hexagon. Joining parts never changes a shape.
• B (correct): The line joins the middle of the flat side of the half-circle to the middle of a side of the hexagon, the same spots as points M and N in the left box; turning a shape does not move a point on it.
• C: The line ends in the wrong place: it meets the half-circle at the top of the curved side, but point M is at the middle of the flat side.
• D: The line ends in the wrong place: it meets the half-circle at a corner of the flat side, but point M is at the middle of the flat side.

Answer: C

Check one letter at a time. Point J is at the middle of a slanted side of the trapezoid, and point K is at a sharp corner of the parallelogram. Cross out any figure where either end of the line lands somewhere else or where a shape has changed. The shapes may be turned, so find each point by its place on the shape (corner, middle of a side, center), not by up, down, left or right.

• A: The line ends in the wrong place: it meets the trapezoid at a corner of the short side, but point J is at the middle of a slanted side.
• B: The line ends in the wrong place: it meets the trapezoid at a corner of the long side, but point J is at the middle of a slanted side and it meets the parallelogram at the center, but point K is at a sharp corner.
• C (correct): The line joins the middle of a slanted side of the trapezoid to a sharp corner of the parallelogram, the same spots as points J and K in the left box; turning a shape does not move a point on it.
• D: The line ends in the wrong place: it meets the parallelogram at the middle of a short side, but point K is at a sharp corner.

Answer: B

Check one letter at a time. Point X is at a wide corner of the diamond, and point Y is at the middle of a side of the pentagon. Cross out any figure where either end of the line lands somewhere else or where a shape has changed. The shapes may be turned, so find each point by its place on the shape (corner, middle of a side, center), not by up, down, left or right.

• A: The line ends in the wrong place: it meets the diamond at the middle of a side, but point X is at a wide corner.
• B (correct): The line joins a wide corner of the diamond to the middle of a side of the pentagon, the same spots as points X and Y in the left box; turning a shape does not move a point on it.
• C: One of the shapes here is a hexagon, but the left box has a pentagon. Joining parts never changes a shape.
• D: The line ends in the wrong place: it meets the pentagon at a corner, but point Y is at the middle of a side.

Answer: D

Check one letter at a time. Point M is at a sharp corner of the diamond, and point N is at the center of the hexagon. Cross out any figure where either end of the line lands somewhere else or where a shape has changed. The shapes may be turned, so find each point by its place on the shape (corner, middle of a side, center), not by up, down, left or right.

• A: The line ends in the wrong place: it meets the diamond at the middle of a side, but point M is at a sharp corner.
• B: One of the shapes here is a pentagon, but the left box has a hexagon. Joining parts never changes a shape.
• C: The line ends in the wrong place: it meets the hexagon at a corner, but point N is at the center.
• D (correct): The line joins a sharp corner of the diamond to the center of the hexagon, the same spots as points M and N in the left box; turning a shape does not move a point on it.

Answer: B

Check one letter at a time. Point V is at the middle of the shorter leg of the right triangle, and point W is at the center of the rectangle. Cross out any figure where either end of the line lands somewhere else or where a shape has changed. The shapes may be turned, so find each point by its place on the shape (corner, middle of a side, center), not by up, down, left or right.

• A: The line ends in the wrong place: it meets the right triangle at the sharpest corner, but point V is at the middle of the shorter leg.
• B (correct): The line joins the middle of the shorter leg of the right triangle to the center of the rectangle, the same spots as points V and W in the left box; turning a shape does not move a point on it.
• C: One of the shapes here is a square, but the left box has a rectangle. Joining parts never changes a shape.
• D: The line ends in the wrong place: it meets the right triangle at the middle of the longer leg, but point V is at the middle of the shorter leg.

Answer: D

Check one letter at a time. Point J is at a corner of the triangle, and point K is at the middle of a slanted side of the trapezoid. Cross out any figure where either end of the line lands somewhere else or where a shape has changed. The shapes may be turned, so find each point by its place on the shape (corner, middle of a side, center), not by up, down, left or right.

• A: The line ends in the wrong place: it meets the triangle at the center, but point J is at a corner and it meets the trapezoid at the middle of the short side, but point K is at the middle of a slanted side.
• B: The line ends in the wrong place: it meets the trapezoid at the middle of the long side, but point K is at the middle of a slanted side.
• C: The line ends in the wrong place: it meets the triangle at the middle of a side, but point J is at a corner.
• D (correct): The line joins a corner of the triangle to the middle of a slanted side of the trapezoid, the same spots as points J and K in the left box; turning a shape does not move a point on it.

Answer: D

Check one letter at a time. Point J is at the middle of a side of the hexagon, and point K is at a corner of the flat side of the half-circle. Cross out any figure where either end of the line lands somewhere else or where a shape has changed. The shapes may be turned, so find each point by its place on the shape (corner, middle of a side, center), not by up, down, left or right.

• A: The line ends in the wrong place: it meets the half-circle at the middle of the flat side, but point K is at a corner of the flat side.
• B: One of the shapes here is a pentagon, but the left box has a hexagon. Joining parts never changes a shape.
• C: The line ends in the wrong place: it meets the hexagon at the center, but point J is at the middle of a side.
• D (correct): The line joins the middle of a side of the hexagon to a corner of the flat side of the half-circle, the same spots as points J and K in the left box; turning a shape does not move a point on it.

Answer: C

Check one letter at a time. Point T is at the middle of a side of the triangle, and point U is at the peak of the roof of the house shape. Cross out any figure where either end of the line lands somewhere else or where a shape has changed. The shapes may be turned, so find each point by its place on the shape (corner, middle of a side, center), not by up, down, left or right.

• A: The line ends in the wrong place: it meets the house shape at the middle of the bottom side, but point U is at the peak of the roof.
• B: The line ends in the wrong place: it meets the triangle at a corner, but point T is at the middle of a side and it meets the house shape at the middle of a wall, but point U is at the peak of the roof.
• C (correct): The line joins the middle of a side of the triangle to the peak of the roof of the house shape, the same spots as points T and U in the left box; turning a shape does not move a point on it.
• D: The line ends in the wrong place: it meets the house shape at a bottom corner, but point U is at the peak of the roof.

Answer: D

Check one letter at a time. Point P is at a corner of the square, and point Q is at the middle of the longer leg of the right triangle. Cross out any figure where either end of the line lands somewhere else or where a shape has changed. The shapes may be turned, so find each point by its place on the shape (corner, middle of a side, center), not by up, down, left or right.

• A: The line ends in the wrong place: it meets the square at the center, but point P is at a corner.
• B: One of the shapes here is a rectangle, but the left box has a square. Joining parts never changes a shape.
• C: The line ends in the wrong place: it meets the right triangle at the right-angle corner, but point Q is at the middle of the longer leg.
• D (correct): The line joins a corner of the square to the middle of the longer leg of the right triangle, the same spots as points P and Q in the left box; turning a shape does not move a point on it.

Answer: D

Check one letter at a time. Point G is at the peak of the roof of the house shape, and point H is at the middle of a short side of the parallelogram. Cross out any figure where either end of the line lands somewhere else or where a shape has changed. The shapes may be turned, so find each point by its place on the shape (corner, middle of a side, center), not by up, down, left or right.

• A: The line ends in the wrong place: it meets the house shape at the middle of a wall, but point G is at the peak of the roof and it meets the parallelogram at a sharp corner, but point H is at the middle of a short side.
• B: The line ends in the wrong place: it meets the house shape at a bottom corner, but point G is at the peak of the roof.
• C: The line ends in the wrong place: it meets the house shape at the middle of the bottom side, but point G is at the peak of the roof.
• D (correct): The line joins the peak of the roof of the house shape to the middle of a short side of the parallelogram, the same spots as points G and H in the left box; turning a shape does not move a point on it.

Answer: B

Check one letter at a time. Point P is at a corner of the flat side of the half-circle, and point Q is at a bottom corner of the house shape. Cross out any figure where either end of the line lands somewhere else or where a shape has changed. The shapes may be turned, so find each point by its place on the shape (corner, middle of a side, center), not by up, down, left or right.

• A: The line ends in the wrong place: it meets the half-circle at the middle of the flat side, but point P is at a corner of the flat side.
• B (correct): The line joins a corner of the flat side of the half-circle to a bottom corner of the house shape, the same spots as points P and Q in the left box; turning a shape does not move a point on it.
• C: The line ends in the wrong place: it meets the half-circle at the top of the curved side, but point P is at a corner of the flat side and it meets the house shape at the middle of the bottom side, but point Q is at a bottom corner.
• D: The line ends in the wrong place: it meets the house shape at a corner where the roof meets a wall, but point Q is at a bottom corner.

Answer: C

Check one letter at a time. Point G is at a corner of the long side of the trapezoid, and point H is at the center of the triangle. Cross out any figure where either end of the line lands somewhere else or where a shape has changed. The shapes may be turned, so find each point by its place on the shape (corner, middle of a side, center), not by up, down, left or right.

• A: The line ends in the wrong place: it meets the trapezoid at a corner of the short side, but point G is at a corner of the long side and it meets the triangle at the middle of a side, but point H is at the center.
• B: The line ends in the wrong place: it meets the trapezoid at a corner of the short side, but point G is at a corner of the long side.
• C (correct): The line joins a corner of the long side of the trapezoid to the center of the triangle, the same spots as points G and H in the left box; turning a shape does not move a point on it.
• D: The line ends in the wrong place: it meets the triangle at the middle of a side, but point H is at the center.

Answer: C

Check one letter at a time. Point G is at the middle of the longer leg of the right triangle, and point H is at the middle of a side of the diamond. Cross out any figure where either end of the line lands somewhere else or where a shape has changed. The shapes may be turned, so find each point by its place on the shape (corner, middle of a side, center), not by up, down, left or right.

• A: The line ends in the wrong place: it meets the diamond at a wide corner, but point H is at the middle of a side.
• B: The line ends in the wrong place: it meets the diamond at a sharp corner, but point H is at the middle of a side.
• C (correct): The line joins the middle of the longer leg of the right triangle to the middle of a side of the diamond, the same spots as points G and H in the left box; turning a shape does not move a point on it.
• D: The line ends in the wrong place: it meets the right triangle at the sharpest corner, but point G is at the middle of the longer leg and it meets the diamond at a sharp corner, but point H is at the middle of a side.

Answer: D

Check one letter at a time. Point G is at the center of the diamond, and point H is at a corner of the hexagon. Cross out any figure where either end of the line lands somewhere else or where a shape has changed. The shapes may be turned, so find each point by its place on the shape (corner, middle of a side, center), not by up, down, left or right.

• A: The line ends in the wrong place: it meets the diamond at the middle of a side, but point G is at the center.
• B: The line ends in the wrong place: it meets the diamond at a wide corner, but point G is at the center.
• C: The line ends in the wrong place: it meets the diamond at a sharp corner, but point G is at the center and it meets the hexagon at the center, but point H is at a corner.
• D (correct): The line joins the center of the diamond to a corner of the hexagon, the same spots as points G and H in the left box; turning a shape does not move a point on it.

Answer: D

Check one letter at a time. Point V is at a corner of the flat side of the half-circle, and point W is at the middle of the short side of the trapezoid. Cross out any figure where either end of the line lands somewhere else or where a shape has changed. The shapes may be turned, so find each point by its place on the shape (corner, middle of a side, center), not by up, down, left or right.

• A: The line ends in the wrong place: it meets the trapezoid at the middle of the long side, but point W is at the middle of the short side.
• B: The line ends in the wrong place: it meets the half-circle at the middle of the flat side, but point V is at a corner of the flat side and it meets the trapezoid at a corner of the short side, but point W is at the middle of the short side.
• C: The line ends in the wrong place: it meets the trapezoid at a corner of the long side, but point W is at the middle of the short side.
• D (correct): The line joins a corner of the flat side of the half-circle to the middle of the short side of the trapezoid, the same spots as points V and W in the left box; turning a shape does not move a point on it.

Answer: A

Check one letter at a time. Point R is at the center of the diamond, and point S is at a corner of the long side of the trapezoid. Cross out any figure where either end of the line lands somewhere else or where a shape has changed. The shapes may be turned, so find each point by its place on the shape (corner, middle of a side, center), not by up, down, left or right.

• A (correct): The line joins the center of the diamond to a corner of the long side of the trapezoid, the same spots as points R and S in the left box; turning a shape does not move a point on it.
• B: One of the shapes here is a square, but the left box has a diamond. Joining parts never changes a shape.
• C: The line ends in the wrong place: it meets the diamond at a sharp corner, but point R is at the center.
• D: The line ends in the wrong place: it meets the diamond at the middle of a side, but point R is at the center.

Answer: A

Check one letter at a time. Point M is at the middle of a short side of the rectangle, and point N is at the middle of a side of the triangle. Cross out any figure where either end of the line lands somewhere else or where a shape has changed. The shapes may be turned, so find each point by its place on the shape (corner, middle of a side, center), not by up, down, left or right.

• A (correct): The line joins the middle of a short side of the rectangle to the middle of a side of the triangle, the same spots as points M and N in the left box; turning a shape does not move a point on it.
• B: One of the shapes here is a parallelogram, but the left box has a rectangle. Joining parts never changes a shape.
• C: The line ends in the wrong place: it meets the rectangle at a corner, but point M is at the middle of a short side.
• D: The line ends in the wrong place: it meets the rectangle at the middle of a long side, but point M is at the middle of a short side.

Answer: D

Check one letter at a time. Point P is at the center of the parallelogram, and point Q is at a corner of the square. Cross out any figure where either end of the line lands somewhere else or where a shape has changed. The shapes may be turned, so find each point by its place on the shape (corner, middle of a side, center), not by up, down, left or right.

• A: The line ends in the wrong place: it meets the parallelogram at the middle of a short side, but point P is at the center.
• B: One of the shapes here is a rectangle, but the left box has a square. Joining parts never changes a shape.
• C: The line ends in the wrong place: it meets the parallelogram at the middle of a long side, but point P is at the center.
• D (correct): The line joins the center of the parallelogram to a corner of the square, the same spots as points P and Q in the left box; turning a shape does not move a point on it.

Answer: A

Check one letter at a time. Point R is at a corner of the square, and point S is at a sharp corner of the parallelogram. Cross out any figure where either end of the line lands somewhere else or where a shape has changed. The shapes may be turned, so find each point by its place on the shape (corner, middle of a side, center), not by up, down, left or right.

• A (correct): The line joins a corner of the square to a sharp corner of the parallelogram, the same spots as points R and S in the left box; turning a shape does not move a point on it.
• B: The line ends in the wrong place: it meets the parallelogram at the center, but point S is at a sharp corner.
• C: One of the shapes here is a rectangle, but the left box has a square. Joining parts never changes a shape.
• D: The line ends in the wrong place: it meets the square at the center, but point R is at a corner.

Answer: D

Check one letter at a time. Point E is at a corner of the flat side of the half-circle, and point F is at the right-angle corner of the right triangle. Cross out any figure where either end of the line lands somewhere else or where a shape has changed. The shapes may be turned, so find each point by its place on the shape (corner, middle of a side, center), not by up, down, left or right.

• A: The line ends in the wrong place: it meets the right triangle at the middle of the slanted side, but point F is at the right-angle corner.
• B: The line ends in the wrong place: it meets the right triangle at the middle of the shorter leg, but point F is at the right-angle corner.
• C: The line ends in the wrong place: it meets the half-circle at the top of the curved side, but point E is at a corner of the flat side.
• D (correct): The line joins a corner of the flat side of the half-circle to the right-angle corner of the right triangle, the same spots as points E and F in the left box; turning a shape does not move a point on it.

Answer: A

Check one letter at a time. Point J is at the center of the triangle, and point K is at a sharp corner of the parallelogram. Cross out any figure where either end of the line lands somewhere else or where a shape has changed. The shapes may be turned, so find each point by its place on the shape (corner, middle of a side, center), not by up, down, left or right.

• A (correct): The line joins the center of the triangle to a sharp corner of the parallelogram, the same spots as points J and K in the left box; turning a shape does not move a point on it.
• B: The line ends in the wrong place: it meets the triangle at a corner, but point J is at the center and it meets the parallelogram at a wide corner, but point K is at a sharp corner.
• C: The line ends in the wrong place: it meets the parallelogram at the middle of a long side, but point K is at a sharp corner.
• D: The line ends in the wrong place: it meets the parallelogram at a wide corner, but point K is at a sharp corner.

Answer: A

Check one letter at a time. Point R is at the center of the hexagon, and point S is at the middle of the long side of the trapezoid. Cross out any figure where either end of the line lands somewhere else or where a shape has changed. The shapes may be turned, so find each point by its place on the shape (corner, middle of a side, center), not by up, down, left or right.

• A (correct): The line joins the center of the hexagon to the middle of the long side of the trapezoid, the same spots as points R and S in the left box; turning a shape does not move a point on it.
• B: The line ends in the wrong place: it meets the hexagon at a corner, but point R is at the center and it meets the trapezoid at the middle of a slanted side, but point S is at the middle of the long side.
• C: The line ends in the wrong place: it meets the trapezoid at a corner of the long side, but point S is at the middle of the long side.
• D: The line ends in the wrong place: it meets the hexagon at the middle of a side, but point R is at the center.

Answer: D

Check one letter at a time. Point V is at a corner of the triangle, and point W is at a corner of the rectangle. Cross out any figure where either end of the line lands somewhere else or where a shape has changed. The shapes may be turned, so find each point by its place on the shape (corner, middle of a side, center), not by up, down, left or right.

• A: The line ends in the wrong place: it meets the triangle at the middle of a side, but point V is at a corner.
• B: The line ends in the wrong place: it meets the rectangle at the middle of a short side, but point W is at a corner.
• C: One of the shapes here is a square, but the left box has a rectangle. Joining parts never changes a shape.
• D (correct): The line joins a corner of the triangle to a corner of the rectangle, the same spots as points V and W in the left box; turning a shape does not move a point on it.

Answer: B

Check one letter at a time. Point G is at a sharp corner of the diamond, and point H is at the middle of a wall of the house shape. Cross out any figure where either end of the line lands somewhere else or where a shape has changed. The shapes may be turned, so find each point by its place on the shape (corner, middle of a side, center), not by up, down, left or right.

• A: The line ends in the wrong place: it meets the diamond at the center, but point G is at a sharp corner and it meets the house shape at the peak of the roof, but point H is at the middle of a wall.
• B (correct): The line joins a sharp corner of the diamond to the middle of a wall of the house shape, the same spots as points G and H in the left box; turning a shape does not move a point on it.
• C: The line ends in the wrong place: it meets the diamond at a wide corner, but point G is at a sharp corner.
• D: The line ends in the wrong place: it meets the house shape at a bottom corner, but point H is at the middle of a wall.

Answer: A

Check one letter at a time. Point M is at the center of the square, and point N is at the middle of a short side of the parallelogram. Cross out any figure where either end of the line lands somewhere else or where a shape has changed. The shapes may be turned, so find each point by its place on the shape (corner, middle of a side, center), not by up, down, left or right.

• A (correct): The line joins the center of the square to the middle of a short side of the parallelogram, the same spots as points M and N in the left box; turning a shape does not move a point on it.
• B: The line ends in the wrong place: it meets the square at a corner, but point M is at the center.
• C: One of the shapes here is a diamond, but the left box has a square. Joining parts never changes a shape.
• D: The line ends in the wrong place: it meets the parallelogram at a sharp corner, but point N is at the middle of a short side.

Answer: D

Check one letter at a time. Point K is at a corner of the hexagon, and point L is at a corner of the short side of the trapezoid. Cross out any figure where either end of the line lands somewhere else or where a shape has changed. The shapes may be turned, so find each point by its place on the shape (corner, middle of a side, center), not by up, down, left or right.

• A: The line ends in the wrong place: it meets the trapezoid at the middle of the short side, but point L is at a corner of the short side.
• B: The line ends in the wrong place: it meets the hexagon at the middle of a side, but point K is at a corner.
• C: One of the shapes here is a pentagon, but the left box has a hexagon. Joining parts never changes a shape.
• D (correct): The line joins a corner of the hexagon to a corner of the short side of the trapezoid, the same spots as points K and L in the left box; turning a shape does not move a point on it.

Answer: A

Check one letter at a time. Point P is at a corner of the flat side of the half-circle, and point Q is at the center of the rectangle. Cross out any figure where either end of the line lands somewhere else or where a shape has changed. The shapes may be turned, so find each point by its place on the shape (corner, middle of a side, center), not by up, down, left or right.

• A (correct): The line joins a corner of the flat side of the half-circle to the center of the rectangle, the same spots as points P and Q in the left box; turning a shape does not move a point on it.
• B: The line ends in the wrong place: it meets the rectangle at the middle of a long side, but point Q is at the center.
• C: One of the shapes here is a square, but the left box has a rectangle. Joining parts never changes a shape.
• D: The line ends in the wrong place: it meets the half-circle at the top of the curved side, but point P is at a corner of the flat side.

Answer: B

Check one letter at a time. Point G is at the center of the parallelogram, and point H is at a corner of the flat side of the half-circle. Cross out any figure where either end of the line lands somewhere else or where a shape has changed. The shapes may be turned, so find each point by its place on the shape (corner, middle of a side, center), not by up, down, left or right.

• A: One of the shapes here is a rectangle, but the left box has a parallelogram. Joining parts never changes a shape.
• B (correct): The line joins the center of the parallelogram to a corner of the flat side of the half-circle, the same spots as points G and H in the left box; turning a shape does not move a point on it.
• C: The line ends in the wrong place: it meets the parallelogram at the middle of a long side, but point G is at the center.
• D: The line ends in the wrong place: it meets the half-circle at the top of the curved side, but point H is at a corner of the flat side.

Answer: A

Check one letter at a time. Point V is at the middle of a side of the diamond, and point W is at the right-angle corner of the right triangle. Cross out any figure where either end of the line lands somewhere else or where a shape has changed. The shapes may be turned, so find each point by its place on the shape (corner, middle of a side, center), not by up, down, left or right.

• A (correct): The line joins the middle of a side of the diamond to the right-angle corner of the right triangle, the same spots as points V and W in the left box; turning a shape does not move a point on it.
• B: The line ends in the wrong place: it meets the right triangle at the middle of the longer leg, but point W is at the right-angle corner.
• C: The line ends in the wrong place: it meets the diamond at a wide corner, but point V is at the middle of a side.
• D: The line ends in the wrong place: it meets the diamond at a sharp corner, but point V is at the middle of a side and it meets the right triangle at the middle of the shorter leg, but point W is at the right-angle corner.

Answer: B

Check one letter at a time. Point R is at the middle of the flat side of the half-circle, and point S is at the middle of a side of the pentagon. Cross out any figure where either end of the line lands somewhere else or where a shape has changed. The shapes may be turned, so find each point by its place on the shape (corner, middle of a side, center), not by up, down, left or right.

• A: The line ends in the wrong place: it meets the pentagon at the center, but point S is at the middle of a side.
• B (correct): The line joins the middle of the flat side of the half-circle to the middle of a side of the pentagon, the same spots as points R and S in the left box; turning a shape does not move a point on it.
• C: The line ends in the wrong place: it meets the half-circle at the top of the curved side, but point R is at the middle of the flat side.
• D: One of the shapes here is a hexagon, but the left box has a pentagon. Joining parts never changes a shape.

Answer: A

Check one letter at a time. Point P is at the middle of a side of the square, and point Q is at the top of the curved side of the half-circle. Cross out any figure where either end of the line lands somewhere else or where a shape has changed. The shapes may be turned, so find each point by its place on the shape (corner, middle of a side, center), not by up, down, left or right.

• A (correct): The line joins the middle of a side of the square to the top of the curved side of the half-circle, the same spots as points P and Q in the left box; turning a shape does not move a point on it.
• B: The line ends in the wrong place: it meets the half-circle at a corner of the flat side, but point Q is at the top of the curved side.
• C: The line ends in the wrong place: it meets the square at a corner, but point P is at the middle of a side.
• D: One of the shapes here is a diamond, but the left box has a square. Joining parts never changes a shape.

Answer: B

Check one letter at a time. Point K is at a corner of the triangle, and point L is at a corner of the pentagon. Cross out any figure where either end of the line lands somewhere else or where a shape has changed. The shapes may be turned, so find each point by its place on the shape (corner, middle of a side, center), not by up, down, left or right.

• A: The line ends in the wrong place: it meets the pentagon at the center, but point L is at a corner.
• B (correct): The line joins a corner of the triangle to a corner of the pentagon, the same spots as points K and L in the left box; turning a shape does not move a point on it.
• C: The line ends in the wrong place: it meets the triangle at the middle of a side, but point K is at a corner.
• D: One of the shapes here is a hexagon, but the left box has a pentagon. Joining parts never changes a shape.

Answer: B

Check one letter at a time. Point E is at a corner of the long side of the trapezoid, and point F is at a wide corner of the diamond. Cross out any figure where either end of the line lands somewhere else or where a shape has changed. The shapes may be turned, so find each point by its place on the shape (corner, middle of a side, center), not by up, down, left or right.

• A: The line ends in the wrong place: it meets the trapezoid at the middle of a slanted side, but point E is at a corner of the long side and it meets the diamond at a sharp corner, but point F is at a wide corner.
• B (correct): The line joins a corner of the long side of the trapezoid to a wide corner of the diamond, the same spots as points E and F in the left box; turning a shape does not move a point on it.
• C: The line ends in the wrong place: it meets the diamond at the center, but point F is at a wide corner.
• D: The line ends in the wrong place: it meets the diamond at the middle of a side, but point F is at a wide corner.

Answer: A

Check one letter at a time. Point K is at a corner of the rectangle, and point L is at a sharp corner of the diamond. Cross out any figure where either end of the line lands somewhere else or where a shape has changed. The shapes may be turned, so find each point by its place on the shape (corner, middle of a side, center), not by up, down, left or right.

• A (correct): The line joins a corner of the rectangle to a sharp corner of the diamond, the same spots as points K and L in the left box; turning a shape does not move a point on it.
• B: The line ends in the wrong place: it meets the rectangle at the middle of a short side, but point K is at a corner and it meets the diamond at a wide corner, but point L is at a sharp corner.
• C: The line ends in the wrong place: it meets the rectangle at the middle of a short side, but point K is at a corner.
• D: The line ends in the wrong place: it meets the diamond at the middle of a side, but point L is at a sharp corner.

Answer: D

Check one letter at a time. Point J is at the right-angle corner of the right triangle, and point K is at the peak of the roof of the house shape. Cross out any figure where either end of the line lands somewhere else or where a shape has changed. The shapes may be turned, so find each point by its place on the shape (corner, middle of a side, center), not by up, down, left or right.

• A: The line ends in the wrong place: it meets the house shape at the middle of a wall, but point K is at the peak of the roof.
• B: The line ends in the wrong place: it meets the right triangle at the middle of the longer leg, but point J is at the right-angle corner and it meets the house shape at a bottom corner, but point K is at the peak of the roof.
• C: The line ends in the wrong place: it meets the house shape at the middle of the bottom side, but point K is at the peak of the roof.
• D (correct): The line joins the right-angle corner of the right triangle to the peak of the roof of the house shape, the same spots as points J and K in the left box; turning a shape does not move a point on it.

Answer: A

Check one letter at a time. Point E is at the middle of the short side of the trapezoid, and point F is at the top of the curved side of the half-circle. Cross out any figure where either end of the line lands somewhere else or where a shape has changed. The shapes may be turned, so find each point by its place on the shape (corner, middle of a side, center), not by up, down, left or right.

• A (correct): The line joins the middle of the short side of the trapezoid to the top of the curved side of the half-circle, the same spots as points E and F in the left box; turning a shape does not move a point on it.
• B: The line ends in the wrong place: it meets the trapezoid at a corner of the long side, but point E is at the middle of the short side and it meets the half-circle at the middle of the flat side, but point F is at the top of the curved side.
• C: The line ends in the wrong place: it meets the half-circle at a corner of the flat side, but point F is at the top of the curved side.
• D: The line ends in the wrong place: it meets the trapezoid at a corner of the long side, but point E is at the middle of the short side.