EXAMPLE 1 o o o Find hypotenuse length

EXAMPLE 1 o o o Find hypotenuse length in a 45 -45 -90 triangle Find the length of the hypotenuse. a. SOLUTION a. By the Triangle Sum Theorem, the measure of the o o 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. hypotenuse = leg =8 2 2 o o o 45 -45 -90 Triangle Theorem Substitute.

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

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

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

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

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

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

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

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