1. 7.4 Similarity in Right Triangles

2. Theorem 7.3
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 C B D A

3. Vocabulary Geometric mean - the number x such that
, where a, b and x are positive numbers

4. Example
Find the geometric mean of 4 and 18

5. Try it
Find the geometric mean of 3 and 48

6. Corollary 1 to Theorem 7.3
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

7. Corollary 2 to Theorem 7.3
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

8. Solve for x and y x y 5 4

9. Answer
Use Corollary 2 to solve for x
Use corollary 1 to solve for y

10. Solve for x and y 4 x 12 y

11. Answer
Use Corollary 2 to solve for x
Use corollary 1 to solve for y

12. Classwork/Homework
Pgs #2-22 even, even