9 3 AltitudeOnHypotenuse Theorems Objective After studying this

9. 3 Altitude-On-Hypotenuse Theorems Objective: After studying this section, you will be able to identify the relationships between the parts of a right triangle when an altitude is drawn to the hypotenuse

When altitude CD is drawn to the hypotenuse of triangle ABC, three similar triangles are formed. C D A B C A D B Therefore, AC is the mean proportional between AB and AD

C A D B Therefore, CB is the mean proportional between AB and DB C C A DD B Therefore, CD is the mean proportional between AD and DB

Theorem 68: If an altitude is drawn to the hypotenuse of a right triangle, then a. The two triangles formed are similar to the given right triangle and to each other. b. The altitude to the hypotenuse is the mean proportional between the segments of the hypotenuse. C b A y a h D x c B

c. Either leg of the given right triangle is the mean proportional between the hypotenuse of the given right triangle and the segment of the hypotenuse adjacent to that leg (i. e. the projection of that leg on the hypotenuse) C a B y b h D x c A

Example 1 If AD = 3 and DB = 9, find CD C A Example 2 If AD = 3 and DB = 9, find AC D B

Example 3 If DB = 21 and AC = 10, find AD C A D B

Given: P R J Prove: (PO)(PM) = (PR)(PJ) 1. ) Given 4. ) Given 5. ) Def altitude 7. ) Reasons 1 -6 8. ) Transitive Prop. O K M

Summary: Summarize what you learned from today’s lesson. Homework: Worksheet 9. 3