1. Chapter 9: Right Triangles and Trigonometry Lesson 9.1: Similar Right Triangles

2. Theorems Thm 9.1: If the altitude is drawn to the hypotenuse of a right triangle, then the two triangles formed are similar to the original triangle and to each other.

3. Theorems Thm 9.2: In a right triangle, the altitude from the right angle to the hypotenuse divides the hypotenuse into two segments. The length of the altitude is the geometric mean of the lengths of the two segments

4. Theorems Thm 9.3: In a right triangle, the altitude from the right angle to the hypotenuse divides the hypotenuse into two segments. The length of each leg of the right triangle is the geometric mean of the lengths of the hypotenuse and the segment of the hypotenuse that is adjacent to the leg.

5. Example 1: A roof has a cross section that is a right triangle. T he diagram shows the approximate dimensions of this cross section. 12.3 m 14.6 m h 7.8 m a)Identify the similar triangles in the diagram b)Find the height, h, of the roof. a)  ABD ~  BCD ~  ACB b) 14.6h = 95.94 h = 6.6 m A D C B

6. Example 2: Find the value of each variable x 610 a) X 2 = 60 x = y 5 8 Y 2 = 65 y = b)