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o. o. o. Find hypotenuse length in a 45-45-90 triangle. a. a. 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. o. o. o. o. o. o. o. - PowerPoint PPT Presentation
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EXAMPLE 1 Find hypotenuse length in a 45-45-90 triangleo o o
Find the length of the hypotenuse.a.
SOLUTION
hypotenuse = leg 2
= 8 2 Substitute.
45-45-90 Triangle Theoremo 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.
o oooa.
EXAMPLE 1 Find hypotenuse length in a 45-45-90 triangleo o o
hypotenuse = leg 2
Substitute.
45-45-90 Triangle Theoremo o o
= 3 2 2= 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 - 90ooo
Find the length of the hypotenuse.b.
EXAMPLE 2 Find leg lengths in a 45-45-90 triangleo 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 - 90ooo
hypotenuse = leg 2
Substitute.
45-45-90 Triangle Theoremo o o
25 = x 2
252
=2x2
5 = x
Divide each side by 2
Simplify.
EXAMPLE 3 Standardized Test Practice
SOLUTION
By the Corollary to the Triangle Sum Theorem, the triangle is a triangle.45 - 45 - 90
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EXAMPLE 3 Standardized Test Practice
hypotenuse = leg 2
Substitute.
45-45-90 Triangle Theoremo o o
= 25 2WX
The correct answer is B.
GUIDED PRACTICE for Examples 1,2 and 3
Find the value of the variable.
1.
SOLUTION
hypotenuse = leg 2
Substitute.
45-45-90 Triangle Theoremo o o
222
=2x2
2 = x
Divide each side by 2
Simplify.
22 = 2x
By the Base Angles Theorem and the Corollary to the Triangle Sum Theorem, the triangle is a triangle.
45 - 45 - 90ooo
GUIDED PRACTICE for Examples 1,2 and 3
Find the value of the variable.
2.
SOLUTION
hypotenuse = leg 2
Substitute.
45-45-90 Triangle Theoremo o o
Simplify.
= 2y 2
y = 2
By the Base Angles Theorem and the Corollary to the Triangle Sum Theorem, the triangle is a triangle.
45 - 45 - 90ooo
GUIDED PRACTICE for Examples 1,2 and 3
Find the value of the variable.
3.
SOLUTION
hypotenuse = leg 2
Substitute.
45-45-90 Triangle Theoremo o o
Simplify.
= 2d 8
d = 8 2
By the Base Angles Theorem and the Corollary to the Triangle Sum Theorem, the triangle is a triangle.
45 - 45 - 90ooo
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 Theoremo o o
Substitute.
Divide each side by 2
Simplify.
= leg 26
223 = leg 2
23 = leg
By the Base Angles Theorem and the Corollary to the Triangle Sum Theorem, the triangle is a triangle.
45 - 45 - 90ooo
