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MCRBG-0901-PE.qxd
3-16-2001
3:03 PM
Page 160
LESSON
9.1
NAME _________________________________________________________ DATE ____________
Practice with Examples For use with pages 527–534
GOAL
Solve problems involving similar right triangles formed by the altitude drawn to the hypotenuse of a right triangle and use a geometric mean to solve problems Theorem 9.1 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. Theorem 9.2 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. Theorem 9.3 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 a geometric mean of the lengths of the hypotenuse and the segment of the hypotenuse that is adjacent to the leg.
EXAMPLE 1
Finding the Height of a Triangle Consider the right triangle shown.
B
a. Identify the similar triangles.
D
11.6
b. Find the height h of ABC.
6 h
SOLUTION a. ABC~CBD~ACD
A
C
10
Sketch the three similar right triangles so that the corresponding angles and sides have the same orientation. B
C
B
C
D A
D A
C
b. Use the fact that ABC~CBD to write a proportion.
Chapter 9
CD CB AC AB h 6 10 11.6 11.6h 610 h 5.2
160
Geometry Practice Workbook with Examples
Corresponding side lengths are in proportion. Substitute. Cross product property Solve for h.
