7.4 Similarity in Right Triangles February 18, 2010
7.4 Similarity in Right Triangles
Objective: To find and use relationships in similar right triangles.
Feb 11­7:46 AM
1
7.4 Similarity in Right Triangles February 18, 2010
Warmup
Name the three right triangles in the figure below.
C
A
D
B
Feb 11­8:03 AM
2
7.4 Similarity in Right Triangles February 18, 2010
Similarity in Right Triangles
B
B
C
D
D
A
A
B
D
C
C
C
A
Feb 11­8:14 AM
3
7.4 Similarity in Right Triangles February 18, 2010
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
D
C
A
D
Feb 11­8:54 AM
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7.4 Similarity in Right Triangles February 18, 2010
Write the proportionality statements for each set of similar triangles.
a
b
h
r
s
c
a
a
r
b
b
h
s
h
Short leg & Hypotenuse Long leg & Hypotenuse Long leg & Short leg
Large to Medium
Large to Small
Medium to Small
Feb 11­11:51 AM
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7.4 Similarity in Right Triangles February 18, 2010
Example #1
x
4
5
y
y
x
4 +
5
Step 1: Separate each triangle and orient correctly.
Step 2: Set up the proportionality statement.
Step 3: Solve the proportion.
Feb 12­8:19 AM
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7.4 Similarity in Right Triangles February 18, 2010
Example #2
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.
Feb 12­8:30 AM
7
7.4 Similarity in Right Triangles February 18, 2010
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:
Feb 12­8:37 AM
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7.4 Similarity in Right Triangles February 18, 2010
Physical Representation of Geometric Mean
h
3
9
9
h
3
h
Feb 12­8:49 AM
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7.4 Similarity in Right Triangles February 18, 2010
Geometric Mean (continued)
b
6
10
16
b
6
b
Feb 13­12:09 PM
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7.4 Similarity in Right Triangles February 18, 2010
Geometric Mean (continued)
a
2
a
5
10
a
5
Feb 13­3:49 PM
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7.4 Similarity in Right Triangles February 18, 2010
Example #3
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?
Feb 13­4:15 PM
12
7.4 Similarity in Right Triangles February 18, 2010
We done.
(except . . .)
Feb 13­4:35 PM
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7.4 Similarity in Right Triangles February 18, 2010
Homework
Pg. 394
# 1 ­ 7 odd, 9 ­ 20, 22, 34 ­ 36
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14