7.4_Similarity_in_right_triangles.notebook
February 23, 2010
7.4 Similarity in Right Triangles
Objective: To find and use relationships in similar right triangles.
Warmup
Name the three right triangles in the figure below.
C
A
D
B
1
7.4_Similarity_in_right_triangles.notebook
February 23, 2010
Similarity in Right Triangles
C
A
B
D
D
Appropriately label each side of the three similar triangles. Then give the similarity statement. C
b
B
A
a
h
r
s
B
D
c
B
C
C
A
C
D
A
D
2
7.4_Similarity_in_right_triangles.notebook
February 23, 2010
Write the proportionality statements for each set of similar triangles.
a
b
h
r
s
c
c
a
a
r
b
h
s
h
Short leg & Hypotenuse Long leg & Hypotenuse Long leg & Short leg
b
Large to Medium
Large to Small
Medium to Small
Practice
Step 1: Separate each triangle and orient correctly.
x
x
y
y
4
4 + 5
Step 2: Set up the proportionality statement.
5
Step 3: Solve the proportion.
3
7.4_Similarity_in_right_triangles.notebook
February 23, 2010
Practice
Step 1: Separate each triangle and orient correctly.
x
16
4
x
y
y
12
Step 2: Set up the proportionality statement.
Step 3: Solve the proportion.
New Vocabulary: Geometric mean
a
x
The geometric mean of a and b is the positive number x such that . x = b
Find the geometric mean of:
4 and 9:
3 and 18:
5 and 9:
4
7.4_Similarity_in_right_triangles.notebook
February 23, 2010
Physical representation of geometric mean
h
9
3
9
h
3
h
Geometric mean cont.
b
6
10
16
b
b
6
5
7.4_Similarity_in_right_triangles.notebook
February 23, 2010
Geometric mean cont.
a
5
2
a
10
a
5
Example
a. A service station will be built on the highway, and a road will connect it with Cray. How far from Blare should the service station be located so that the proposed road will be perpendicular to the highway?
b. How long will the new road be?
6
7.4_Similarity_in_right_triangles.notebook
February 23, 2010
We done.
(except . . .)
Homework
Pg. 394
# 1 ­ 7 odd, 9 ­ 20, 22, 34 ­ 36
7