Download 8.3 Practice with Examples

LESSON
8.3
NAME _________________________________________________________ DATE ____________
Practice with Examples
For use with pages 473–479
GOAL
Identify and use similar polygons
VOCABULARY
When there is a correspondence between two polygons such that their
corresponding angles are congruent and the lengths of corresponding
sides are proportional the two polygons are called similar polygons.
Theorem 8.1 If two polygons are similar, then the ratio of their
perimeters is equal to the ratios of their corresponding side lengths.
EXAMPLE 1
Writing Similarity Statements
Quadrilaterals ABCD and EFGH are similar. A
List all the pairs of congruent angles. Write
the ratios of the corresponding sides in a
statement of proportionality.
B
D
SOLUTION
E
C
F
H
G
Because ABCD ~ EFGH you can writeA E, B F, C G, and
D H. You can write the statement of proportionality as follows:
AB
BC
CD
DA
.
EF FG GH HE
Exercises for Example 1
The two polygons are similar. List all the pairs of congruent angles.
Write the ratios of the corresponding sides in a statement of
proportionality.
2. ABDC ~ ZWXY
A
B
3. EFGHJ ~ MRQPN
B
G
F
H
Q
F
A
X
D
C
Y
D
J
E
R
P
C
E
Copyright © McDougal Littell Inc.
All rights reserved.
W
Z
N
Geometry
Practice Workbook with Examples
M
145
Chapter 8
1. ABC ~ DEF
LESSON
8.3
CONTINUED
EXAMPLE 2
NAME _________________________________________________________ DATE ____________
Practice with Examples
For use with pages 473–479
Comparing Similar Polygons
Decide whether the figures are similar.
If they are similar, write a similarity
statement.
X
B
6
4
2
A
3
C
Z
4
Y
8
SOLUTION
The corresponding angles of ABC and XYZ are congruent. Also, the
corresponding side lengths are proportional.
AB 2 1
XY
4 2
CA 3 1
ZX
6 2
BC 4 1
YZ
8 2
So, the two triangles are similar and you can write ABC ~ XYZ.
Exercises for Example 2
Are the polygons similar? If so, write a similarity statement.
4.
2
A
D
E
B
3
100
2
5.
C
6
B
5
7.5
9
8
G
3
H
F
54
A
Y
45
11
C
11.3
8
3
100
4.5
J
45
X
8
Z
Chapter 8
K
9
146
Geometry
Practice Workbook with Examples
Copyright © McDougal Littell Inc.
All rights reserved.
LESSON
8.3
CONTINUED
EXAMPLE 3
NAME _________________________________________________________ DATE ____________
Practice with Examples
For use with pages 473–479
Using Similar Polygons
Pentagon ABCDE is similar to
pentagon JKLMN. Find the value of x.
B
C
5
D
SOLUTION
N
A
Set up a proportion that contains KL.
AB BC
JK
KL
4
E
M
Write a proportion.
J
6
5 4
6
x
Substitute.
x 4.8
Cross multiply and divide by 5.
K
L
x
Exercises for Example 3
Find the value of x.
7. JKLMN ~ PQRST
6. ABCD ~ WXYZ
C
L
K
D
M
Y
3
B
Z
14
x
J
N
P
x
T
X
6
Q
10
8
A
7
S
W
R
Chapter 8
Copyright © McDougal Littell Inc.
All rights reserved.
Geometry
Practice Workbook with Examples
147