1. CHAPTER 8 RIGHT TRIANGLES
8.4
SPECIAL RIGHT TRIANGLES

2. SPECIAL RIGHT TRIANGLES
We will learn about 2 kinds of triangles that are well known in Geometry:
45° - 45° - 90° triangle, and
30° - 60° - 90° triangle.
These triangles are identified by their angle measures and have sides with specific relationships.

3. THEOREM 8-6
45°
a√2 a a a
45° a a

4. EXAMPLES Find the value of x
10√2
3√2 x
45° 10 x
45° 6

5. THEOREM 8-7 THEOREM 8-7 30° - 60° - 90° Theorem
In a 30° - 60° - 90° triangle, the hypotenuse is twice as long as the shorter leg, and the longer leg is √3 times as long as the short leg.
30° 2a
a√3
60° a

6. EXAMPLE Find x and y. x = 18 x = 3√3 y = 9√3 y = 6√3 9 x x 9 30° 60° y

7. PRACTICE Complete: If r = 6, t = _____ If s = 2√5, t = _____
If t = √2, r = _____
If t = 10, s = _____
6√2
2√10 1
5√2 t r
45° s

8. PRACTICE Complete: 8√3, 16 If q = 8, p = _____ and n = _____. 10, 10√3
4, 8
3√3, 6√3
If q = 8, p = _____ and n = _____.
If n = 20, q = _____ and p = _____.
If p = 4√3, q = _____ and n = _____.
If p = 9, q = _____ and n = _____.
30° n p q

9. PRACTICE
A diagonal of a square has length 6. What is the perimeter of the square?
12√2

10. CLASSWORK/HOMEWORK 8.4 Assignment Pg. 301, Classroom Exercises 1-12
Pg , Written Exercises 2-28 even