1. EXAMPLE 1 Find hypotenuse length in a 45-45-90 triangle o o o Find the length of the hypotenuse. a. SOLUTION hypotenuse = leg 2 = 8 2 Substitute. 45-45-90 Triangle Theorem o o o By the Triangle Sum Theorem, the measure of the third angle must be 45. Then the triangle is a 45-45-90 triangle, so by Theorem 7.8, the hypotenuse is 2 times as long as each leg. oo o o a.

2. EXAMPLE 1 Find hypotenuse length in a 45-45-90 triangle o o o hypotenuse = leg 2 Substitute. 45-45-90 Triangle Theorem o o o = 3 22 = 3 2 Product of square roots = 6 Simplify. b. By the Base Angles Theorem and the Corollary to the Triangle Sum Theorem, the triangle is a triangle. 45 - 45 - 90 o o o Find the length of the hypotenuse. b.

3. EXAMPLE 2 Find leg lengths in a 45-45-90 triangle o o o Find the lengths of the legs in the triangle. SOLUTION By the Base Angles Theorem and the Corollary to the Triangle Sum Theorem, the triangle is a triangle. 45 - 45 - 90 o o o hypotenuse = leg 2 Substitute. 45-45-90 Triangle Theorem o o o 2 5 = x 2 2 5 2 = 2 x 2 5 = x Divide each side by 2 Simplify.

4. EXAMPLE 3 Standardized Test Practice SOLUTION By the Corollary to the Triangle Sum Theorem, the triangle is a triangle. 45 - 45 - 90 o o o

5. EXAMPLE 3 Standardized Test Practice hypotenuse = leg 2 Substitute. 45-45-90 Triangle Theorem o o o = 25 2 WX The correct answer is B.

6. GUIDED PRACTICE for Examples 1,2 and 3 Find the value of the variable. 1. SOLUTION hypotenuse = leg 2 Substitute. 45-45-90 Triangle Theorem o o o 2 2 2 = 2 x 2 2 = x Divide each side by 2 Simplify. 2 2 = 2 x By the Base Angles Theorem and the Corollary to the Triangle Sum Theorem, the triangle is a triangle. 45 - 45 - 90 o o o

7. GUIDED PRACTICE for Examples 1,2 and 3 Find the value of the variable. 2. SOLUTION hypotenuse = leg 2 Substitute. 45-45-90 Triangle Theorem o o o Simplify. = 2 y 2 y = 2 By the Base Angles Theorem and the Corollary to the Triangle Sum Theorem, the triangle is a triangle. 45 - 45 - 90 o o o

8. GUIDED PRACTICE for Examples 1,2 and 3 Find the value of the variable. 3. SOLUTION hypotenuse = leg 2 Substitute. 45-45-90 Triangle Theorem o o o Simplify. = 2 d 8 d = 8 2 By the Base Angles Theorem and the Corollary to the Triangle Sum Theorem, the triangle is a triangle. 45 - 45 - 90 o o o

9. GUIDED PRACTICE for Examples 1,2 and 3 4. Find the leg length of a 45°-45°-90° triangle with a hypotenuse length of 6. SOLUTION hypotenuse = leg 2 45-45-90 Triangle Theorem o o o Substitute. Divide each side by 2 Simplify. = leg 26 22 3 22 3 By the Base Angles Theorem and the Corollary to the Triangle Sum Theorem, the triangle is a triangle. 45 - 45 - 90 o o o