1. 8-3 Special Right Triangles You used properties of isosceles and equilateral triangles. Use the properties of 45°-45°-90° triangles. Use the properties of 30°-60°-90° triangles.

2. Making of an Isosceles Right Triangle #1 How can you make an isosceles right triangle?

3. Right Ratios Use the Pythagorean Theorem to find the third side. 45° 7 7 4 4

4. 45°- 45°- 90° Right Triangle In a 45°- 45°- 90° triangle, the hypotenuse is √2 times as long as either leg. The ratios of the side lengths can be written l-l-l√2. l l p. 558

5. Find the length of the side 10 x r s a b 9 r = s = 4

6. Find x. The given angles of this triangle are 45° and 90°. This makes the third angle 45°, since 180 – 45 – 90 = 45. Thus, the triangle is a 45°-45°-90° triangle. Substitution 45°-45°-90° Triangle Theorem

7. Find x. The legs of this right triangle have the same measure, x, so it is a 45°-45°-90° triangle. Use the 45°-45°-90° Triangle Theorem. Substitution 45°-45°-90° Triangle Theorem x = 12 Answer: x = 12

8. Find x. A.3.5 B.7 C. D.

9. Find x. A. B. C.16 D.32

10. Find a. The length of the hypotenuse of a 45°-45°-90° triangle is times as long as a leg of the triangle. Substitution 45°-45°-90° Triangle Theorem Multiply. Divide. Rationalize the denominator. Divide each side by

11. Making of an Isosceles Right Triangle #2 How can you make an isosceles right triangle? 60°

12. Right Ratios Use the Pythagorean Theorem to find the third side. 12 66 ? 60° 30°

13. 30°- 60° - 90° Right Triangle In a 30°- 60° - 90° triangle, the hypotenuse is twice as long as the shorter leg (the leg opposite the 30° angle, and the longer leg (opposite the 60° angle) is √3 tunes as long as the shorter leg. The ratios of the side lengths can be written l - l√3 – 2l. 60° 30° l 2l p. 560

14. Find the length of the side 30° 60° 30° 60° 30° 60° 30° 60° 4 20 4.8 2l = 8 2l = 20 l = 10 l = 5 2l = 10 2.77 5.54

15. Find BC. A.4 in. B.8 in. C. D.12 in.

16. 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.

17. What two type of right triangles occur often? 30°-60°-90° and 45°-45°-90°. How can you find the length of a side of a special right triangle knowing only one side? 60° 30° l 2l l l

18. 8-3 Assignment Worksheet 5-3B Skip 12-14