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Practice A
8-5 Indirect Measurement
Write the correct answer.
1. Use similar triangles to find the height of the lamppost.
h
5 ft
20 ft
10 ft
2. Use similar triangles to find the height of the man.
h
4 ft
12 ft
8 ft
3. A 3-foot-tall boy looks into a mirror at
the county fair. The mirror makes a
person appear shorter. The boy
appears to be 1 foot tall in the mirror.
If a man appears to be 2 feet tall in
the mirror, what is his actual height?
4. On a sunny day, a carnation casts a
shadow that is 20 inches long. At the
same time, a 3-inch-tall tulip casts a
shadow that is 12 inches long. How
tall is the carnation?
5. A bicycle casts a shadow that is 8
feet long. At the same time, a girl
who is 5 feet tall casts a shadow that
is 10 feet long. How tall is the
bicycle?
6. A sand castle casts a shadow that is
5 inches long. A 15-inch-tall bucket
sitting next to the sand castle casts a
shadow that is 3 inches long. How
tall is the sand castle?
7. Through a magnifying glass, a
2-centimeter-long bug looks like it is
12 centimeters long. How long would
a 3-centimeter bug look in that same
magnifying glass?
8. In the late afternoon, a wagon casts
a shadow that is 15 feet long. A boy
pulling the wagon who is 4 feet tall
casts a shadow that is 20 feet long.
How tall is the wagon?
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
45
Holt Middle School Math Course 1
Puzzles, Twisters & Teasers
8-4 With One Blow!
Problem Solving
8-4 Similar Figures
LESSON
LESSON
Write the correct answer.
Solve each of the problems below and circle your answer.
Transfer the matching letters, in order, on to the blanks to solve
the riddle.
Bermuda
1. The map at right shows the
dimensions of the Bermuda Triangle,
a region of the Atlantic Ocean where
many ships and airplanes have
disappeared. If a theme park makes a
swimming pool in a similar figure, and
the longest side of the pool is 0.5
mile long, about how long would the
other sides of the pool have to be?
mi.
80
1,1
950 mi.
rida
Flo
1. A small triangle has a hypotenuse of 5, and sides of 3 and 4.
A larger, similar, triangle has a hypotenuse of 30. Find the
lengths of the other two sides of the larger triangle.
95
0
mi.
Puerto
Rico
0.403 mile
2. Completed in 1883, The Battle of
Gettysburg is one of the largest
paintings in the world. It is 410 feet
long and 70 feet tall. A museum shop
sells a print of the painting that is
similar to the original. The print is
2.05 feet long. How tall is the print?
3. Panorama of the Mississippi was the
largest painting ever created in the
United States. It was 12 feet tall and
5,000 feet long! If you wanted to
make a copy similar to the original
that was 2 feet tall, how many feet
long would the copy have to be?
1
3
833!! feet
0.35 ft
4. Two tables shaped like triangles are
similar. The measure of one of the
larger table’s angles is 38!, and
another angle is half that size. What
are the measures of all the angles in
the smaller table?
G 24
F 12
W 15
S 20
I 18
2. A large parallelogram has angles of 120 degrees and 60
degrees. What are the corresponding angles of a smaller, similar
parallelogram?
A 120
V 90
R 180
P 30
E 360
N 60
3. Alok went to the photography store to develop some film. He has
three choices of sizes for his prints. He thinks that two of the
sizes make similar rectangles. Which size does not make a
rectangle similar to the other two?
M 4 by 6
5. Two rectangular gardens are similar.
The area of the larger garden is
8.28 m2, and its length is 6.9 m.
The smaller garden is 0.6 m wide.
What is the smaller garden’s length
and area?
38!, 19!, and 123!
K 25
T 8 by 10
B 8 by 12
What kind of ant can break a picnic table with one blow?
A
G
I
A
N
T
length " 3.45 m;
area " 2.07 m2
Circle the letter of the correct answer.
7. Which of the following figures are
always similar?
F two rectangles
G two triangles
H two squares
!
J two pentagons
6. Which of the following is not always
true if two figures are similar?
A They have the same shape.
B They have the same size.
!
C Their corresponding sides have
proportional lengths.
D Their corresponding angles are
congruent.
41
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
Holt Middle School Math Course 1
Exploration Recording Sheet
8-5 Indirect Measurement
42
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
Holt Middle School Math Course 1
Practice A
8-5 Indirect Measurement
LESSON
LESSON
The heights of very tall structures can be
measured indirectly using similar figures and
proportions. This method is called indirect
measurement.
Write the correct answer.
1. Use similar triangles to find the height of the lamppost.
Augustine and Carmen want to measure
the height of the school’s flagpole. To do
this, they go outside and hold a meterstick
upright. The meterstick casts a shadow that
measures 50 cm.
h " 10 feet
h
5 ft
x cm
20 ft
1. If the shadow of the flagpole measures
6 meters, how tall is the flagpole? To
answer this question, follow these steps:
a. Draw a sketch of the flagpole and its
shadow next to the sketch of the
meterstick and its shadow.
10 ft
h " 6 feet
2. Use similar triangles to find the height of the man.
100 cm
50 cm
600 cm
h
4 ft
b. Label the height of the flagpole x.
12 ft
height of flagpole
height of meterstick
c. Write the proportion !!! " !!! ,
shadow of flagpole
shadow of meterstick
8 ft
3. A 3-foot-tall boy looks into a mirror at
the county fair. The mirror makes a
person appear shorter. The boy
appears to be 1 foot tall in the mirror.
If a man appears to be 2 feet tall in
the mirror, what is his actual height?
and substitute the values for the given measurements.
x
100
! ! " !!
600
50
d. Solve the proportion for x.
1,200 cm or 12 m
4. On a sunny day, a carnation casts a
shadow that is 20 inches long. At the
same time, a 3-inch-tall tulip casts a
shadow that is 12 inches long. How
tall is the carnation?
6 feet
Think and Discuss
2. Explain how you solved the proportion for x in Exercise 1d.
Possible answer: The proportion is solved by cross multiplying.
3. Explain whether you could have solved the problem by writing
6. A sand castle casts a shadow that is
5 inches long. A 15-inch-tall bucket
sitting next to the sand castle casts a
shadow that is 3 inches long. How
tall is the sand castle?
4 feet
shadow of flagpole
shadow of meterstick
the proportion as !!! " !!! .
height of flagpole
5 inches
5. A bicycle casts a shadow that is 8
feet long. At the same time, a girl
who is 5 feet tall casts a shadow that
is 10 feet long. How tall is the
bicycle?
height of meterstick
25 inches
7. Through a magnifying glass, a
2-centimeter-long bug looks like it is
12 centimeters long. How long would
a 3-centimeter bug look in that same
magnifying glass?
Possible answer: The proportion could be solved as long as both ratios
are written in the same order.
8. In the late afternoon, a wagon casts
a shadow that is 15 feet long. A boy
pulling the wagon who is 4 feet tall
casts a shadow that is 20 feet long.
How tall is the wagon?
18 cm
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
44
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
Holt Middle School Math Course 1
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
118
3 feet
45
Holt Middle School Math Course 1
Holt Middle School Math Course 1