1. 8-3 Special Right Triangles

2. 8 8

3. 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.

4. EXAMPLE
What is the value of each variable?

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

6. EXAMPLE
What is the value of x?

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

8. 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.

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

10. 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.

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

12. 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.

13. HOMEWORK
Pgs #’s 1-6, 8-25, 28-33