Triangles flashcards

The three interior angles total 180°. Each exterior angle equals the two non-adjacent interior angles added together. With remote angles 45° and 70°, the exterior angle is 115° and the adjacent interior angle is 65°.

No. The sum of the two shorter sides has to exceed the longest side, but 5 + 7 = 12 < 13. With two sides a < b, the third side lies strictly between b − a and a + b.

$A=\frac{1}{2}bh$, where b is the base and h is the height perpendicular to that base (not a slanted side); the answer is in square units. Base 10 cm and height 6 cm give 30 cm².

In a right triangle, $a^2+b^2=c^2$, with legs a and b and hypotenuse c (the longest side, opposite the right angle). Legs 6 and 8 give $c=\sqrt{100}=10$. For a missing leg, subtract the squares.

3-4-5, 5-12-13, 8-15-17 and 7-24-25, plus any whole-number multiple of them, such as 6-8-10 or 10-24-26. Spotting one gives the missing side without square roots.

45-45-90: $1:1:\sqrt{2}$, so hypotenuse = leg $\times \sqrt{2}$. 30-60-90: $1:\sqrt{3}:2$; the short leg is half the hypotenuse and the long leg is short leg $\times \sqrt{3}$. Hypotenuse 14: legs 7 and $7\sqrt{3}$.

With scale factor k, every length (sides, perimeter, heights) is multiplied by k, but area is multiplied by $k^2$. Doubling every side of a 12 cm² triangle gives 48 cm², not 24 cm².

Valid: SSS, SAS, ASA, AAS, and HL for right triangles. Not valid: SSA, which can fit two different triangles, and AAA, which fixes the shape but not the size.