Geometry Chapter 9
Section 9.1 ­ Similar Right Triangles
C
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.
A
D
B
CBD ~ ABC, ACD ~ ABC, and CBD ~ ACD
A
Example 1
1. Identify the similar triangles
11.6
10
B
h
2. Find the height of ACD.
C
D
6
3. Find the height of the given triangle
a.
b.
C
4
h
A
D
5
E
3
2
2
h
B
D
G
2
F
1
Theorem 9.2
C
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
B
D
AD CD
CD = BD
Theorem 9.3
C
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 length of the hypotenuse and the segment of the hypotenuse that is adjacent to the leg.
A
D
B
AB AC
AC = AD
AB CB
=
CB DB
Example 2
Find the value of each variable.
C
a.
z
A
10
Homework:
C
b.
z
x
y
D
A
B
4
3
Page: 531
x
y
D
B
1
Problem: 1­30
2