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LESSON
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Date
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Practice C
8-4 Similar Figures
The figures in each pair are similar. Find the unknown
measures.
1.
5 in.
w
7 in.
9.1 in.
2.
Z
A
?
3 ft
C
48°
x
3 ft
48°
4 ft
B
3.
X
?
84°
12 ft
?
16 ft
Y
18cm
M
N
?
12.6 cm
9cm
6cm
B
110° x
?
C
P
9cm
A
3cm
D
4.
?
27cm
S
20 in.
C
W
90°
53°
25 in.
L
90°
10 in.
15 in.
?
O
K
37°
7.5 in.
? E
x
5. Two regular pentagons are similar. One side of the
first pentagon is 3 m long, and the perimeter of the
second pentagon is three times as long as the first
pentagon. What are the lengths of each side of the
second pentagon?
6. A 7-by-9 foot rectangle is similar to a second rectangle
whose perimeter is 260 ft. What are the dimensions
of the second rectangle?
Copyright © by Holt, Rinehart and Winston.
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38
Holt Middle School Math Course 1
Practice C
8-4 Similar Figures
Practice B
8-4 Similar Figures
LESSON
LESSON
Write the correct answers.
The figures in each pair are similar. Find the unknown
measures.
1. The two triangles are similar. Find the missing
length x and the measure of !A.
x ! 18 ft; m!A ! 80°
1.
D
32°
B
30 ft
?
20 ft
5 in.
w
80°
A
7 in.
x ft
12 ft
68°
22 ft
C
32°
E
F
33 ft
2.
Z
A
2. The two triangles are similar. Find the missing
length x and the measure of !J.
C
18 m
12 m
23°
P
122°
x
122°
M
K
H
12 m
D
4.
20 in.
12 cm
?
11 cm
G
N
Y
18cm
N
12.6 cm
?
27cm
S
x
20 cm
67°
?
16 ft
9cm
6cm
B
110° x
?
C
P
9cm
A
3cm
x ! 24 cm; m!N ! 53°
60°
L
?
12 ft
53°
67°
C
H
22 cm
W
90°
?
53°
25 in.
L
90°
10 in.
15 in.
K
37°
7.5 in.
? E
x
!C ! 37°, !E ! 53°, x ! 12.5 in.
4. Juanita planted two flower gardens in similar square shapes.
What are the measures of all the angles in each garden?
Explain how you know.
5. Two regular pentagons are similar. One side of the
first pentagon is 3 m long, and the perimeter of the
second pentagon is three times as long as the first
pentagon. What are the lengths of each side of the
second pentagon?
They are all 90°; All squares have all right angles.
9 meters
6. A 7-by-9 foot rectangle is similar to a second rectangle
whose perimeter is 260 ft. What are the dimensions
of the second rectangle?
37
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
O
m!C ! 70°, m!N ! 110°, m!O ! 70°, x ! 4.2 cm
M
10 cm
X
M
J
60°
B
4 ft
84°
?
35°
3. The two triangles are similar. Find the missing
length x and the measure of !N.
3 ft
48°
3.
15 m
35°
48°
x
m!A ! 84°, m!X ! 48°, m!Y ! 48°, x ! 12 ft
?
10 m
?
3 ft
x ! 8m; m!J ! 23°
J
N
9.1 in.
w ! 6.5 in.
68°
Holt Middle School Math Course 1
Reteach
8-4 Similar Figures
38
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
56.875 ft by 73.125 ft
Holt Middle School Math Course 1
Challenge
8-4 You Won’t Believe Your Eyes!
LESSON
LESSON
Two figures are similar if they have the same shape but are different
sizes.
Answer each question by looking at the drawings below.
Then use what you know about similar and congruent figures
to verify your answers.
Similar figures have corresponding sides and corresponding angles.
Corresponding sides are proportional. Corresponding angles are
congruent.
1.
2.
Look at the similar triangles below.
P
A
3
48°
B
C
4
Q
Are the two line segments
congruent?
10
6
5
?
yes
R
x
A
!B
! corresponds to P
!Q
!.
B
!C
! corresponds to Q
!R
!.
AC
!
! corresponds to P
!R
!.
Are the two center circles similar or
congruent?
congruent
3.
!A corresponds to !P.
!B corresponds to !Q.
!C corresponds to !R.
4.
What is the length of !
QR
!?
AB
PQ
!! ! !!
BC
QR
3
6
!! ! !!
4
x
Set up a proportion.
Substitute the values.
3•x!4•6
Are any of these circles similar?
The cross products are equal.
3x ! 24
x is multiplied by 3.
3x
24
!! ! ! !
3
3
Divide both sides by 3.
Are any of these line segments
congruent?
yes; all the circles
yes; horizontal lines
5.
x!8
6.
So, the length of !
QR
! is 8 units.
Find each missing length.
1. F
2
G
2.
I
8
J
H
B
6
K
x
X
12
C
24
L
Which horizontal line is longer?
Which two figures are congruent?
Which two figures are similar?
Neither, they are congruent.
congruent circles; similar
squares
x ! 26 units
x ! 24 units
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
13
x
10
Y
V
W
A
5
39
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
Holt Middle School Math Course 1
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
117
40
Holt Middle School Math Course 1
Holt Middle School Math Course 1