The Pythagorean Theorem

In a right triangle with legs a and b and hypotenuse c: [formula] The hypotenuse is always the longest side and is opposite the right angle. Common Pythagorean triples (memorize these!): - 3, 4, 5 (and multiples: 6, 8, 10; 9, 12, 15; etc.) - 5, 12, 13 - 8, 15, 17 - 7, 24, 25 Converse: If a^2 + b^2 = c^2, the triangle is a right triangle.

Example: A right triangle has legs 6 and 8. Find the hypotenuse.

If you see a right triangle on the SAT, always check if it's a multiple of a Pythagorean triple. 5, 12, 13 and 3, 4, 5 appear constantly. A triangle with legs 15 and 20 has hypotenuse 25 (it's 3, 4, 5 × 5). Recognizing triples is faster than computing.