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**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.

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**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.

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**Find leg lengths in a 45-45-90 triangle EXAMPLE 2**

o 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.

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**Standardized Test Practice**

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

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**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.

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

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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

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