1. Similarity in Right Triangles 7-4

2. Warmup activity (don’t need to turn in) Complete activity on p. 391 with a partner

3. Theorem In a right triangle, the altitude to the hypotenuse yields three similar triangles. A B C D

4. Example a d b c e f a f b d a b c e e

5. Write an extended proportion for the sides in the medium and small triangles. A C B D

6. Geometric Mean Proportions in which the means are equal occur frequently in geometry. For any two positive numbers a and b, the geometric mean of a and b is the positive number such that Note that

7. Examples – Finding the geometric mean Find the geometric mean of the following numbers (round to two decimal places): a. 4 and 18b. 15 and 20c. 3 and 12

8. Corollary 1 The lengths of the altitude to the hypotenuse of a right triangle is the geometric mean of the lengths of the segments of the hypotenuse.

9. Proof of Corollary 1 *Bonus* Prove

10. Examples Find the missing variables: 50 40 x x4 6

11. Corollary 2 When the altitude to the hypotenuse of a right triangle separates the hypotenuse, the length of each leg is the geometric mean of the length of the adjacent hypotenuse segment and the length of the hypotenuse.

12. Applying Corollaries 1 and 2 Solve for x and y and z.You try x y 45 z x 12 z 4 y

13. Hwk P. 394-395: 1-20, 34-36,49-51