1. Section 8-1 Similarity in Right Triangles

2. Geometric Mean If a, b, and x are positive numbers and Then x is the geometric mean. x and x are the means a and b are the extremes

3. Example: Find the geometric mean between 5 and 11. 1. Set up a proportion: 2. Cross Multiply: 3. Solve: *Simplify the radical if possible!

4. Theorem 8-1 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.

5. A NB C

6. Corollary 1 When the altitude is drawn to the hypotenuse of a right triangle, the length of the altitude is the geometric mean between the segments of the hypotenuse.

7. A NB C

8. Corollary 2 When the altitude is drawn to the hypotenuse of a right triangle, each leg is the geometric mean between the hypotenuse and the segment of the hypotenuse that is adjacent to that leg.

9. A NB C So we can say: or