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

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

3. Find leg lengths in a 45-45-90 triangle EXAMPLE 2o
EXAMPLE 2
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. o
Triangle Theorem o
hypotenuse = leg 2 2 5
= x
Substitute. 2 5 = x
Divide each side by 2
5 = x
Simplify.

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

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

6. GUIDED PRACTICE
for Examples 1, 2, and 3
Find the value of the variable. 1. 2. 3.
ANSWER 2
ANSWER 2 8 2
ANSWER

7. 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. 3 2
ANSWER