NAME
DATE
7-3
PERIOD
Study Guide and Intervention
Similar Triangles
Identify Similar Triangles
Here are three ways to show that two triangles are similar.
AA Similarity
Two angles of one triangle are congruent to two angles of another triangle.
SSS Similarity
The measures of the corresponding side lengths of two triangles are proportional.
SAS Similarity
The measures of two side lengths of one triangle are proportional to the measures of two
corresponding side lengths of another triangle, and the included angles are congruent.
Example 1
Determine whether the
triangles are similar.
A
B
8
6
15
D
10
9
Example 2
Determine whether the
triangles are similar.
3
12
C
Q
M
E
N
70°
F
AC
6
2
−
=−
=−
4
P
6
R
70°
S
8
3
6
MN
NP
−
=−
, so −
=−
.
9
3
DF
BC
8
2
−=−=−
12
3
EF
10
AB
2
−
=−=−
15
3
DE
4
8
QR
RS
m∠N = m∠R, so ∠N ∠R.
NMP ∼ RQS by SAS Similarity.
ABC ∼ DEF by SSS Similarity.
Exercises
B
1.
K
2.
W
E
A
C
D
20
J
F
24
L
F
18
N
39
26
9
Z
J
yes; KDJ ∼ RPZ; SAS Similarity
6.
16
24
G
24
M
E
I
yes; BFE ∼ NLM; SAS Similarity
Chapter 7
R 65°
K
yes; RTU ∼ STL; AA Similarity
B
P
4
65°
L
5.
Y
18
8
T
U
18
L
D
4.
S
X
36
20
no; −
≠−
yes; ABC ∼ DEF; AA Similarity
3. R
36
24
32
40
H
Q 20 R
15
25
S
yes; IGH ∼ SQR; SSS Similarity
18
Glencoe Geometry
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Determine whether the triangles are similar. If so, write a similarity statement.
Explain your reasoning.
NAME
DATE
7-3
PERIOD
Study Guide and Intervention (continued)
Similar Triangles
Use Similar Triangles
Similar triangles can be used to find measurements.
Example 1
Example 2
A person 6 feet tall casts
a 1.5-foot-long shadow at the same time
that a flagpole casts a 7-foot-long
shadow. How tall is the flagpole?
ABC ∼ DEF. Find the
values of x and y.
B
y
A
D
C
18 √⎯
3
E
18
18
9
F
x
AC
BC
−
=−
BC
AB
−
=−
DF
EF
18 √3
18
−=−
x
9
DE
EF
y
18
−=−
18
9
3)
18x = 9(18 √
1.5 ft
9y = 324
x = 9 √
3
?
6 ft
7 ft
The Sun’s rays form similar triangles.
6
1.5
Using x for the height of the pole, −
=−
,
x
7
so 1.5x = 42 and x = 28.
The flagpole is 28 feet tall.
y = 36
Exercises
1. JL
K
Y
35
10
13
X
Z
J
2. IU
20
x
L
36
W 13
U
GIU ˜ GHW; 30
E
V
x
24
R
x
26
4. BC
2
36 √⎯
Q
20
G
XYZ ˜ JKL; 26
3. QR
T
I
H
A
36
38.6
23
30
S
60
B
x
D
C
5. LM
SQV ˜ SRT; 12
K
9
V
6. QP
BED ˜ BCA; 19.3
R
L
x
7.2
8 P
16
Lesson 7-3
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
ALGEBRA Identify the similar triangles. Then find each measure.
F
M
10
N
30
22
32
Q x P
2
FRQ ˜ FNP; 10 −
KVM ˜ LPM; 18
3
7. The heights of two vertical posts are 2 meters and 0.45 meter. When the shorter post
casts a shadow that is 0.85 meter long, what is the length of the longer post’s shadow
to the nearest hundredth? 3.78 m
Chapter 7
19
Glencoe Geometry