1. 5-7 The Pythagorean Theorem
Geometry

2. 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

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

4. 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

5. 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

6. 5-7-1 Converse of the Pythagorean Theorem

7. 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.

8. 5-7-2 Pythagorean Inequalities Theorem

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

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