Name
LESSON
Date
Class
Problem Solving
5-6 Similar Figures and Proportions
Use the information in the table to solve problems 1–3.
1. A small reproduction of one of the
paintings in the list is similar in size.
The reproduction measures
11 inches by 10 inches. Of which
painting is this a reproduction?
2. A local artist painted a reproduction
of Cézanne’s painting. It measures
88 inches by 72 inches. Is the
reproduction similar to the original?
What is the ratio of corresponding
sides?
Original
Size (in.)
Painting
Artist
Mona Lisa
Leonardo
da Vinci
30 by 21
The Dance
Class
Edgar Degas
33 by 30
The Blue
Vase
Paul
Cézanne
22 by 18
3. A poster company made a poster of
da Vinci’s painting. The poster is
5 feet long and 3.5 feet wide. Is the
poster similar to the original Mona
Lisa? What is the ratio of
corresponding sides?
Choose the letter for the best answer.
4. Triangle ABC has sides of 15 cm,
20 cm, and 25 cm. Which triangle
could be similar to triangle ABC?
A A triangle with sides of 3 cm,
4 cm, and 5 cm
B A triangle with sides of 5 cm,
6 cm, and 8 cm
C A triangle with sides of 30 cm,
40 cm, and 55 cm
D A triangle with sides of 5 cm,
10 cm, and 30 cm
5. A rectangular picture frame is
14 inches long and 4 inches wide.
Which dimensions could a similar
picture frame have?
F Length = 21 in.; width = 8 in.
G Length = 35 in.; width = 15 in.
H Length = 49 in.; width = 14 in.
J Length = 7 in.; width = 3 in.
6. A rectangle is 12 meters long and
21 meters wide. Which dimensions
correspond to a nonsimilar
rectangle?
A 4 m; 7 m
C 20 m; 35 m
D 24 m; 35 m
B 8 m; 14 m
7. A rectangle is 6 feet long and 15 feet
wide. Which dimensions correspond
to a similar rectiangle?
F 8 ft; 24 ft
H 15 ft; 35 ft
J 18 ft; 40 ft
G 10 ft; 25 ft
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54
Holt Mathematics
Problem Solving
5-6 Similar Figures and Proportions
Challenge
5-6 The Same, Only Bigger
LESSON
LESSON
Use the information in the table to solve problems 1–3.
You can sometimes create a similar figure by using copies of the original figure.
1. A small reproduction of one of the
paintings in the list is similar in size.
The reproduction measures
11 inches by 10 inches. Of which
painting is this a reproduction?
Notice that the scale factor
tells you how many times
to repeat the original figure
along each side or edge of
the similar figure.
Original Similar Figure
Figure Scale factor = 2
The Dance Class
Original Similar Figure
Figure Scale factor = 3
Use the given scale factor and copies of the original figure to
draw a figure similar to the original figure.
1.
2. A local artist painted a reproduction
of Cézanne’s painting. It measures
88 inches by 72 inches. Is the
reproduction similar to the original?
What is the ratio of corresponding
sides?
2.
Mona Lisa
Leonardo
da Vinci
30 by 21
The Dance
Class
Edgar Degas
33 by 30
The Blue
Vase
Paul
Cézanne
22 by 18
yes; 1:2
Choose the letter for the best answer.
3.
4.
scale factor 2
scale factor 3
5. Draw a figure in the space below. Use a scale factor of 2 to
create a similar figure. Drawings will vary. Possible drawing
given.
53
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Holt Mathematics
4. Triangle ABC has sides of 15 cm,
20 cm, and 25 cm. Which triangle
could be similar to triangle ABC?
A A triangle with sides of 3 cm,
4 cm, and 5 cm
B A triangle with sides of 5 cm,
6 cm, and 8 cm
C A triangle with sides of 30 cm,
40 cm, and 55 cm
D A triangle with sides of 5 cm,
10 cm, and 30 cm
5. A rectangular picture frame is
14 inches long and 4 inches wide.
Which dimensions could a similar
picture frame have?
F Length = 21 in.; width = 8 in.
G Length = 35 in.; width = 15 in.
H Length = 49 in.; width = 14 in.
J Length = 7 in.; width = 3 in.
6. A rectangle is 12 meters long and
21 meters wide. Which dimensions
correspond to a nonsimilar
rectangle?
A 4 m; 7 m
C 20 m; 35 m
D 24 m; 35 m
B 8 m; 14 m
7. A rectangle is 6 feet long and 15 feet
wide. Which dimensions correspond
to a similar rectiangle?
F 8 ft; 24 ft
H 15 ft; 35 ft
J 18 ft; 40 ft
G 10 ft; 25 ft
LESSON
Pretend this is a game of concentration. The object of the game
is to match cards with similar figures. Each box represents a
card with a figure on it. When you match 2 cards, cross them out.
Rearrange the letters of the unmatched cards to solve the riddle.
Similar means almost the same. If two objects are similar, they have
some things in common.
Similar figures are figures that are nearly the same. Similar figures
have the same shape, but are different sizes.
Similar figures have corresponding sides and corresponding
angles. Corresponding means matching. Each side and angle in a
similar figure has a corresponding side and angle.
R
21
50
40
H
60
A
60
21
K
C
R
5
20
I
S
6
A
4
B
F
4
E 3 F
Y
8
Use the figures above to answer each question.
D
1. What angle corresponds to angle B?
12
W 15
S
9
X
10
15
G
J
27
D
4
R
M
I
6
V
15
5
U
8
X
Y
X
W
C
J
8
56
56
Y
9
Z
N
L
angle D
7.5
K
S
6.5
N
7
3. What side corresponds to side BC?
C
T
G
L
M
7
3
E
50
50
side EF
U
M
9
I
4
16
yes
O
J
4
4m
5m
4m
L
J
no
5.
3m
P
K
5m
6m
3
5
S
20
T
15
L
K
5m
10
P
15
R
G
20
O
O
Are the figures similar? Answer yes or no for each pair.
2m
Y
V
T
angle E
2. What angle corresponds to angle A?
4.
U 2
50
H
6
G
I
These two triangles are similar.
A
10
Holt Mathematics
Puzzles, Twisters & Teasers
5-6 Concentrating on Figures
Reading Strategies
5-6 Understanding Vocabulary
8
54
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
LESSON
B
Artist
3. A poster company made a poster of
da Vinci’s painting. The poster is
5 feet long and 3.5 feet wide. Is the
poster similar to the original Mona
Lisa? What is the ratio of
corresponding sides?
yes; 1:4
scale factor 2
scale factor 4
Original
Size (in.)
Painting
6
Q
N
6
M
12
9
I
L
15
O
K
L
What kind of flowers are on your face?
T
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All rights reserved.
55
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
Holt Mathematics
U
L
I
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All rights reserved.
98
P
S
56
Holt Mathematics
Holt Mathematics