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Congruent and Similar Figures
BEFORE
Now
WHY?
You classified polygons by their
angles and by their sides.
You’ll identify similar and
congruent figures.
So you can compare images, such
as the photographs in Ex. 13.
Use the triangles below to answer the questions.
Word Watch
congruent, p. 454
similar, p. 454
corresponding parts, p. 455
4 in.
2 in.
4 in.
4 in.
4 in.
2 in.
3 in.
4 in.
1 Which triangles are the same size and the same shape? Are their angle
measures the same? Are their side lengths the same?
2 Which triangles are the same shape but different sizes? Are their angle
measures the same? Are their side lengths the same?
Comparing Figures Two figures are congruent if they have the
same size and shape. Two figures are similar if they have the same shape
but not necessarily the same size.
EXAMPLE
1
Congruent and Similar Triangles
Tell whether the triangles are similar, congruent, or neither.
F
A
C
K
L
B
H
M
G
Solution
ABC, FGH, and KLM are similar because they have the same
shape. ABC and KLM are congruent because they have the same
size and shape.
Your turn now
or neither.
1.
454
Chapter 9
Geometric Figures
Tell whether the triangles are similar, congruent,
2.
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Corresponding Parts When two figures are similar, their
corresponding angles have the same measure. When two figures are
congruent, their corresponding parts have the same measure.
Corresponding parts are the matching sides and angles of two figures.
EXAMPLE
2
Listing Corresponding Parts
T ABC and T DEF are congruent. List the corresponding parts.
D
A
C
B
E
F
When listing corresponding parts, list corresponding vertices in the same
order.
Corresponding angles: aA and aD, aB and aE, aC and aF
&* and DE
&*, BC
&* and EF
&*, AC
&* and DF
&*
Corresponding sides: AB
EXAMPLE
3
Using Corresponding Parts
Bridges In the photograph, TABC
and TDBC are congruent.
&* is about 51 meters long, how
a. If AC
&* ? Why?
long is DC
b. If maA 50, what is maD ? Why?
Solution
a. Corresponding sides of congruent
triangles have the same length. So,
&* has a length of about 51 meters.
DC
b. Corresponding angles of congruent triangles
have the same measure. So, maD 50.
The Sunshine Skyway
Bridge in Florida
Your turn now
T GHJ and T KML are similar. List the corresponding
parts. Then find maG and maL.
3.
G
L
?
H
50
28
J
Lesson 9.7
?
50
M
102
K
Congruent and Similar Figures
455
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INTERNET
Exercises
eWorkbook Plus
CLASSZONE.COM
More Practice, p. 716
Getting Ready to Practice
Vocabulary Tell whether the statement is true or false.
1. TVUW is congruent to TYXZ
V
because they have the same
size and shape.
Y
2. TVUW is similar to TYXZ.
U
W
X
Z
&
&* corresponds to YX
&&.
3. In the figures, VW
Algebra The two figures are congruent. Find the values of x and y.
4.
5.
4m
10 m
4m
6 yd
x
5 yd
6 yd
y
10 m
4m
10 m
x
y
4 yd
Practice and Problem Solving
with
Example
1
2
3
Homework
Exercises
6–8, 13
9–10
11–12
Tell whether the triangles are similar, congruent, or neither.
6.
7.
8.
3m
5m
11 in.
10 in.
6m
15 in.
6m
5m
11 in.
8 in.
Online Resources
3m
CLASSZONE.COM
• More Examples
• eTutorial Plus
15 in.
List the corresponding parts of the triangles.
9.
A
10 m
8m
10.
D
8m
M
H
10 m
L
G
B
6m
C
F
6m
K
J
E
Algebra The figures are congruent. Find the values of x and y.
11.
12 ft
13 ft
y
5 ft
12 ft
456
Chapter 9
12.
5 ft
x
Geometric Figures
x
4 mi
6 mi
y
60
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13. Photography You are viewing photographs on a computer screen at a
scale of 2 in. : 1 in. Are the images on the screen and the actual
photographs similar? congruent? Explain.
Decide if the objects are usually similar, congruent, or neither. Explain.
14. buttons on your shirt
15. a pair of earrings
16. the drink on the billboard
17. a C battery and
and the actual drink
a AA battery
18. Draw any triangle. Then draw a triangle with the same angle measures
but different side lengths. Are the triangles similar, congruent, or
neither?
19. TXYZ is similar to TABC. List the corresponding parts.
20. Critical Thinking If two figures are congruent, are they also similar?
If two figures are similar, are they also congruent? Explain.
21. Challenge Are all squares similar? Are all rectangles similar? Explain.
Mixed Review
22. Buying CDs A CD that teaches you how to speak Spanish costs $28.75.
There is a 6% sales tax and you have $30. Decide whether you can buy
the CD. (Lesson 8.7)
23. Use a protractor to draw an angle with a measure of 55. (Lesson 9.2)
Basic Skills Find the product or quotient.
24. 3.25 5.6
25. 9.8 0.62
26. 4.85 0.5
Test-Taking Practice
INTERNET
State Test Practice
CLASSZONE.COM
27. Multiple Choice The triangles
shown are congruent. What is the
value of x?
A. 2 cm
B. 3 cm
C. 5 cm
D. 8 cm
x
6 cm
6 cm
6 cm
6 cm
8 cm
28. Multiple Choice The triangles
shown are congruent. Find the
measure of aG.
F. 122
H. 85
D
25
65
G. 88
H
J
25
I. 65
E
Lesson 9.7
F
G
Congruent and Similar Figures
457