1. Warm Up For Exercises 1 and 2, find the value of x. Give your answer in simplest radical form. 1. 2. Simplify expression. 3.

2. Special Right Triangles 8.2 Learning Target: I understand the special cases/ratios of special right triangles without using the Pythagorean Theorem Success Criteria: I can recognize a special right triangle I can use the ratios of special right triangles (45-45- 90 and 30-60-90) to set up proportions to solve real world problems

3. Another Special Triangle

5. Example 1: Finding Side Lengths in a 45 ° - 45º- 90º Triangle Find the value of x. Give your answer in simplest radical form. By the Triangle Sum Theorem, the measure of the third angle in the triangle is 45°. So it is a 45°-45°-90° triangle with a leg length of 8.

6. Example 2: Finding Side Lengths in a 45º- 45º- 90º Triangle Find the value of x. Give your answer in simplest radical form. The triangle is an isosceles right triangle, which is a 45°-45°-90° triangle. The length of the hypotenuse is 5.

7. Example 3 Find the value of x. Give your answer in simplest radical form. x = 20 Simplify. By the Triangle Sum Theorem, the measure of the third angle in the triangle is 45°. So it is a 45°-45°-90° triangle with a leg length of

8. Example 4 Find the value of x. Give your answer in simplest radical form. The triangle is an isosceles right triangle, which is a 45°- 45°-90° triangle. The length of the hypotenuse is 16.

9. A 30°-60°-90° triangle is another special right triangle. You can use an equilateral triangle to find a relationship between its side lengths.

10. Example 5: Finding Side Lengths in a 30º-60º-90º Triangle Find the values of x and y. Give your answers in simplest radical form. Hypotenuse = 2(shorter leg)22 = 2x Divide both sides by 2.11 = x Substitute 11 for x.

11. Example 6 Find the values of x and y. Give your answers in simplest radical form. Hypotenuse = 2(shorter leg) Divide both sides by 2. y = 27Substitute for x.

12. Example 7 Find the values of x and y. Give your answers in simplest radical form. Simplify. y = 2(5) y = 10

13. Example 8 Find the values of x and y. Give your answers in simplest radical form. Hypotenuse = 2(shorter leg) Divide both sides by 2. Substitute 12 for x. 24 = 2x 12 = x

14. Example 9 Find the values of x and y. Give your answers in simplest radical form. Hypotenuse = 2(shorter leg) x = 2y Simplify. Substitute

15. Assignment # 16 Pg 503 #8-12 evens,13,14, 22, 23 – 28

16. Do Now Find the values of the variables. Give your answers in simplest radical form. 1. 2. x = 10; y = 20

17. Lesson Quiz: Part I Find the values of the variables. Give your answers in simplest radical form. 1. 2. 3. 4. x = 10; y = 20

18. Lesson Quiz: Part II Find the perimeter and area of each figure. Give your answers in simplest radical form. 5. a square with diagonal length 20 cm 6. an equilateral triangle with height 24 in.