1. 9.3 Similar Right Triangles

2. Do Now: Draw the altitude and describe what it is.

3. Right Triangle Similarity Theorem If an altitude is drawn, then the two triangles formed are similar to each other and the original triangle.

4. Example 1: Identify the similar triangles.

5. Example 2: Identify the similar triangles.

6. Example 3:Find the value of x.

8. Example 5: A roof has a cross section that is a right triangle. The diagram shows the approximate dimensions of this cross section. Find the height h of the room.

9. Geometric Mean A mean of two positive numbers a and b that is the positive number x that satisfies. So x 2 = ab.

10. Example 6: Find the geometric mean of 24 and 48.

11. Example 7: Find the geometric mean of 8 and 10.

12. Altitude in a Right Triangle In a right triangle, the altitude from the right angle to the hypotenuse divides the hypotenuse into two segments.

13. Geometric Mean (Altitude) Theorem The length of the altitude is the geometric mean of the lengths of the two segments of the hypotenuse.

14. Geometric Mean (Leg) Theorem The length of each leg of the right triangle is the geometric mean of the lengths of the hypotenuse and the segment of hypotenuse that is adjacent to the leg.

15. Example 8: Find the value of x.

16. Example 9: Find the value of y.

17. Example 10: To find the cost of installing a rock wall in your school gymnasium, you need to find the height of the gym wall. You use a cardboard square to line up the top and bottom of the gym wall. Your friend measures the vertical distance from the ground to your eye and the horizontal distance from you to the gym wall. Approximate the height of the gym wall.