1. Chapter 8 Lesson 4 Objective: To find and use relationships in similar right triangles.

2. Theorem 8-3 The altitude to the hypotenuse of a right triangle divides the triangle into two triangles that are similar to the original triangle and to each other. Altitude

3. The geometric mean is the number x such that =, where a, b and x are positive numbers.

4. Example 1: Finding Geometric Mean Find the geometric mean of 4 and 18. The geometric mean of 4 and 18 is 6. What they ask for 1 st. What they ask for 2 nd.

5. Example 2: Finding Geometric Mean Find the geometric mean of 15 and 20.

6. Corollary 1 to Theorem 8-3 The length of the altitude to the hypotenuse of a right triangle is the geometric mean of the lengths of the segments of the hypotenuse. Altitude

7. Corollary 2 to Theorem 8-3 The altitude to the hypotenuse of a right triangle separates the hypotenuse so that the length of each leg of the triangle is the geometric mean of the length of the adjacent hypotenuse segment and the length of the hypotenuse. ∆ACD ~ ∆ABC∆CBD ~ ∆ABC

8. Example 3: Applying Corollaries 1 and 2 Use Corollary 2 to solve for x:Use Corollary 1 to solve for y:

9. Example 4: Applying Corollaries 1 and 2 Solve for x and y. Use Corollary 2 to solve for x:Use Corollary 1 to solve for y:

10. Assignment Pg. 442 #1-20; 26-36