5-7 The Pythagorean Theorem Geometry

The Pythagorean Theorem states, if a and b are the measures of the legs of a right triangle and c is the measure of the hypotenuse, then

Example 1 Find the length of the hypotenuse of each triangle if the measures of the legs are given below. 5 7

Example 2, a If c is the measure of the hypotenuse of a right triangle, find each missing measure. a.) a = 4, c = 10, b = ? B=/84 or 9.17

Example 2, b If c is the measure of the hypotenuse of a right triangle, find each missing measure. b.) a = 10, b = 7, c = ? /51 or 7.14

5-7-1 Converse of the Pythagorean Theorem

Corollary to the Pythagorean Theorem If c is the measure of the longest side of a triangle and then the triangle is NOT a right triangle.

5-7-2 Pythagorean Inequalities Theorem

Example 3, a Determine whether the following side measures would form right triangles. a.) a = 8, b = 9, c = 11 no

Example 3, b Determine whether the following side measures would form right triangles. b.) a = 13, b = 84, c = 85 yes