NAME ______________________________________________ DATE
7-3
____________ PERIOD _____
Practice
Similar Triangles
Determine whether each pair of triangles is similar. Justify your answer.
1.
J
16
Y
42⬚
18
2.
M
K
24
W
L
14
S
16
12
42⬚
A
S
12.5
11
N
18
R
16
T
ALGEBRA Identify the similar triangles, and find x and the measures of the
indicated sides.
3. L
苶M
苶 and Q
苶P
苶
L
4. 苶
NL
苶 and M
苶L
苶
N x⫹5
M
Q
18
x⫺1
N
x⫹3
12
6x ⫹ 2
P
J
8 K
M
L
24
5. If 苶
TS
苶 || Q
苶R
苶, TS ⫽ 6, PS ⫽ x ⫹ 7,
QR ⫽ 8, and SR ⫽ x ⫺ 1,
find PS and PR.
6. If 苶
EF
苶 || H
苶I苶, EF ⫽ 3, EG ⫽ x ⫹ 1,
HI ⫽ 4, and HG ⫽ x ⫹ 3,
find EG and HG.
I
Q
T
G
H
E
P
S
R
F
INDIRECT MEASUREMENT For Exercises 7 and 8, use the following information.
A lighthouse casts a 128-foot shadow. A nearby lamppost that measures 5 feet 3 inches casts
an 8-foot shadow.
7. Write a proportion that can be used to determine the height of the lighthouse.
8. What is the height of the lighthouse?
Chapter 7
24
Glencoe Geometry
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Use the given information to find each measure.
NAME ______________________________________________ DATE
7-3
____________ PERIOD _____
Word Problem Practice
Similar Triangles
1. MINIATURES Marla likes her chair
so much that she decides to make a
miniature replica of it for her pet
hamster. Find the value of x.
4. SHADOWS A radio tower casts a
shadow 8 feet long at the same time
that a vertical yardstick casts a shadow
half an inch long. How tall is the radio
tower?
15”
14”
x
MOUNTAIN PEAKS For Exercises 5 and
3.5”
6, use the following information.
Gavin and Brianna want to know how far a
mountain peak is from their houses. They
measure the angles between the line of site
to the peak and to each other’s houses and
carefully make the drawing shown.
2. MODELS Jim has a scale model of his
sailboat. The figure shows drawings of
the original sailboat and the model.
Find x.
Gavin
0.246 in.
83˚
203 in.
Peak
2.015 in.
Brianna
x in.
The actual distance between Gavin and
1
Brianna’s house is 1ᎏᎏ miles.
52˚
2
10.15 in.
5. What is the actual distance of the
mountain peak from Gavin’s house?
Round your answer to the nearest
tenth of a mile.
8 in.
52˚
3. GEOMETRY Georgia draws a regular
pentagon and starts connecting its
vertices to make a
A
5-pointed star. After
drawing three of the
lines in the star, she D
E
becomes curious
about two triangles
that appear in the
B
C
figure, 䉭ABC and
䉭BCE. They look similar to her. Prove
that this is the case.
Chapter 7
6. What is the actual distance of the
mountain peak from Brianna’s house?
Round your answer to the nearest
tenth of a mile.
25
Glencoe Geometry
Lesson 7-3
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
2 in.
90˚
NAME ______________________________________________ DATE
7-3
____________ PERIOD _____
Enrichment
Moving Shadows
Have you ever watched your shadow as you
walked along the street at night and observed
how its shape changes as you move? Suppose
a man who is 6 feet tall is standing below
a lamppost that is 20 feet tall. The man is
walking away from the lamppost at a rate of
5 feet per second.
1. If the man is moving at a rate of 5 feet per
second, make a conjecture as to the rate
that his shadow is moving.
20 ft
6 ft
5 ft/sec
x ft
2. How far away from the lamppost is the man after 8 seconds?
3. How far is the end of his shadow from the bottom of the lamppost after
8 seconds? Use similar triangles to solve this problem.
5. How many feet did the man move in 3 seconds? How many feet did the shadow
move in 3 seconds?
6. The man is moving at a rate of 5 feet/second. What rate is his shadow moving?
How does this rate compare to the conjecture you made in problem 1? Make a
conjecture as to why the results are like this.
Chapter 7
26
Glencoe Geometry
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
4. After 3 more seconds, how far from the lamppost is the man? How far from the
lamppost is his shadow?