1. How to use the properties of 45º-45º-90º and 30º-60º-90º triangles. Chapter 8.2GeometryStandard/Goal: 4.1

2. 1. Check and discuss assignment from yesterday. 2. Work on Quiz 8.1. 3. Read, write, and discuss how to use the properties of 45º-45º-90º triangles. 4. Read, write, and discuss how to use the properties of 30º-60º-90º triangles. 5. Work on given assignment.

3. In a 45˚ - 45˚ - 90˚ triangle, both legs are congruent and the length of the hypotenuse is times the length of a leg. s s 45˚

4. The length of the hypotenuse is 10 3. h = 2 5 6 hypotenuse = 2 leg h = 5 12Simplify. Find the length of the hypotenuse of a 45°-45°-90° triangle with legs of length 5 6. h = 5 4(3) h = 5(2) 3 h = 10 3 Use the 45°-45°-90° Triangle Theorem to find the hypotenuse. Lesson 8-2

5. 22 2 x = Simplify by rationalizing the denominator. 2 22 2 x = Divide each side by 2. Use the 45°-45°-90° Triangle Theorem to find the leg. x = 11 2Simplify. 22 = 2 leg hypotenuse = 2 leg The length of the leg is 11 2. 22 2 2 x = Find the length of a leg of a 45°-45°-90° triangle with a hypotenuse of length 22. Lesson 8-2

6. The distance from one corner to the opposite corner, 96 ft, is the length of the hypotenuse of a 45°-45°-90° triangle. Each side of the playground is about 68 ft. leg = 67.882251 Use a calculator. 96 = 2 leghypotenuse = 2 leg leg = Divide each side by 2. 96 2 The distance from one corner to the opposite corner of a square playground is 96 ft. To the nearest foot, how long is each side of the playground? Lesson 8-2

7. 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 times the length of the shorter leg. s 60˚ 30˚

8. The length of the shorter leg is 6 3, and the length of the hypotenuse is 12 3. d = 6 3Simplify. f = 2 6 3hypotenuse = 2 shorter leg f = 12 3Simplify. The longer leg of a 30°-60°-90° triangle has length 18. Find the lengths of the shorter leg and the hypotenuse. 18 = 3 shorter leg longer leg = 3 shorter leg d =Divide each side by 3. 18 3 d =Simplify by rationalizing the denominator. 3 18 3 18 3 3 d = Lesson 8-2 You can use the 30°-60°-90° Triangle Theorem to find the lengths.

9. A garden shaped like a rhombus has a perimeter of 100 ft and a 60° angle. Find the area of the garden to the nearest square foot. Because a rhombus has four sides of equal length, each side is 25 ft. Because a rhombus is also a parallelogram, you can use the area formula A = bh. Draw the rhombus with altitude h, and then solve for h. Lesson 8-2

10. h = 12.5 3longer leg = 3 shorter leg A = (25)(12.5 3) Substitute 25 for b and 12.5 3 for h. (continued) The height h is the longer leg of the right triangle. To find the height h, you can use the properties of 30°-60°-90° triangles. Then apply the area formula. To the nearest square foot, the area is 541 ft 2. 25 = 2 shorter leg hypotenuse = 2 shorter leg A = bh Use the formula for the area of a parallelogram. A = 541.26588Use a calculator. shorter leg = = 12.5 Divide each side by 2. 25 2 Lesson 8-2

11. Kennedy, D., Charles, R., Hall, B., Bass, L., Johnson, A. (2009) Geometry Prentice Hall Mathematics. Power Point made by: Robert Orloski Jerome High School.