8-3 Special Right Triangles

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Presentation transcript:

8-3 Special Right Triangles

8 8

45-45-90 Triangles 45-45-90 Triangle Theorem: In a 45-45-90 triangle, both legs are congruent and the length of the hypotenuse is 2 times the length of a leg.

EXAMPLE What is the value of each variable?

EXAMPLE  What is the length of the hypotenuse of a 45-45-90 triangle with leg length 53?

EXAMPLE What is the value of x?

EXAMPLE  The length of the hypotenuse of a 45-45-90 triangle is 10. What is the length of one leg?

30-60-90 Triangles 30-60-90 Triangles Theorem: In a 30-60-90 triangle, the length of the hypotenuse is twice the length of the shorter leg. The length of the longer leg is 3 times the length of the shorter leg.

EXAMPLE 1 What is the value of d in simplest radical form? What is the value of f in simplest radical form?

Example 2 Find Lengths in a 30°-60°-90° Triangle Find x and y. The acute angles of a right triangle are complementary, so the measure of the third angle is 90 – 30 or 60. This is a 30°-60°-90° triangle.

Example 3 Find BC. A. 4 in. B. 8 in. C. D. 12 in.

Example 4 BOOKENDS Shaina designed 2 identical bookends according to the diagram below. Use special triangles to find the height of the bookends. A. B. 10 C. 5 D.

HOMEWORK Pgs. 562-564 #’s 1-6, 8-25, 28-33