1. Section 8.3 Special Right Triangles ! L.T.: Be able to find sides of 45-45-90 triangles! Quick Review: Rationalize the following!

2. 45-45-90 Triangle Theorem: In a 45-45-90 triangle, both ______ are congruent (isosceles), and the length of the hypotenuse is _____ times the length of each leg. Find the length of the hypotenuse: 3 3 8 8 Find the value of each variable: x 45° x y legs 5 x 5

3. x 45° y x y x

4. Find the value of each variable! x 45° y x

5. Find the area of the triangle! 45°

6. Yadier Molina wants to know how far he has to throw the ball to catch a man stealing second. Why do we need to know about 45-45-90 triangles? They are in the real world! Not to mention, it’s a whole lot easier than using the Pythagorean Theorem. 90 ft x ft Before, we had to use the Pythagorean Theorem. But now that you know about 45-45-90 triangles, you can use the shortcut!

7. Find the value of x. x 45° Final Example

8. Quick Review: L.T.: Be able to find sides of 30-60-90 triangles! Section 8.3 Part 2 Special Right Triangles ! x 45° 5 y y x

9. Question: In a 30-60-90 triangle, will any sides be the same length? 30-60-90 Triangle Theorem: In a 30-60-90 triangle,  the length of the hypotenuse is ____ times the length of the shorter leg (shorty)  the length of the longer leg (longy) is _____ times the length of the shorter leg (shorty) “shorty” “longy” hypotenuse 30° 60° No! 2

10. 3 y x 30° Find the value of each variable! x y 7 60° 5 y x 30° y 15 x 30°

11. y 12 x 30° y x 60° 5 y x 30° y 15 x 30°

12. Let’s practice some more! Find the area of each triangle. 6 30° 60°

13. A window-washer leans a 40-foot ladder against the side of a building. The base of the ladder make a 60° angle with the ground. How high up the side of the building does the ladder reach? Find the value of each variable. 60° 45° a b c d 40 ft 60° y x

14. Did we meet the target? Find the value of each variable! L.T.: Be able to find sides of 30-60-90 triangles! 60° 45° a b c d