1. Similar Right Triangles
Advanced Geometry

2. Setting up today’s lesson
Draw a right triangle ABC, with ∠A being the right angle.
Draw the altitude of your triangle from the right angle. Label it AD.

3. Similar Triangles
Given: Right Triangle ABC AD is the altitude of ∆ABC Prove: ∆ABC ~ ∆DBA ~ ∆DAC

4. Right Triangle Similarity Theorem
If the altitude is drawn to the hypotenuse of a right triangle, then the two triangles formed are similar to the original triangle and each other.

5. Example
A roof has a cross section that is a right triangle. The diagram shows the approximate dimensions of this cross section. a. Identify the similar triangles in the diagram. b. Find the height h of the roof. Z W X Y h
5.5
6.3
3.1

6. Geometric Mean Theorems
How do you find the Geometric Mean?

7. Geometric Mean (Altitude) Theorem
In a right triangle. The altitude from the right angle to the hypotenuse divides the hypotenuse into two segments.
The length of the altitude is the geometric mean of the lengths of the two segments. A D B C

8. Geometric Mean (Leg) Theorem
In a right triangle. The altitude from the right angle to the hypotenuse divides the hypotenuse into two segments.
The length of each leg of the right triangle is the geometric mean of the lengths of the hypotenuse and the segment of the hypotenuse that is adjacent to the leg. A D B C

9. Find y 8 2 y

10. Find x x 3 6

11. Find y 5 2 y

12. Example x a b 12 20

13. Find x, y, and z.