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NAME
DATE
7-2
PERIOD
Study Guide and Intervention
Similar Polygons
Identify Similar Polygons
Similar polygons have the same shape but not necessarily
the same size.
Example 1
If ABC ∼ XYZ, list all pairs of congruent angles and
write a proportion that relates the corresponding sides.
:
#
Use the similarity statement.
Congruent angles: ∠A ∠X, ∠B ∠Y, ∠C ∠Z
BC
CA
AB
Proportion: −
=−
=−
XY
YZ
ZX
$
"
9
;
Example 2
Determine whether the pair of figures is similar. If so, write the
similarity statement and scale factor. Explain your reasoning.
Step 1 Compare corresponding angles.
∠W ∠P, ∠X ∠Q, ∠Y ∠R, ∠Z ∠S
Corresponding angles are congruent.
X
12
8 Q
W
Step 2 Compare corresponding sides.
P
8
PQ
2 QR
12
2 RS
10
2
Z
9
3
ZW
−
= −
=−
. Since corresponding sides are proportional,
6
SP
18
9
18
3 YZ
15
3
3 XY
WX
12
−
=−
=−
,−=−
=−
,−=−
=−
, and
15
12
6
S
Y
R
10
2
3
WXYZ ∼ PQRS. The polygons are similar with a scale factor of −
.
2
List all pairs of congruent angles, and write a
proportion that relates the corresponding sides
for each pair of similar polygons.
(
&
%
1. DEF ∼ GHJ
DE
EF
FD
∠D ∠G, ∠E ∠H, ∠F ∠J; −
=−
=−
HJ
JG
GH
'
+
8
3
2. PQRS ∼ TUWX
∠P ∠T, ∠Q ∠U, ∠R ∠W, ∠S ∠X;
PQ
TU
QR
UW
)
RS
SP
− = − =−
=−
WX
4 9
6
2
XT
1
5
Determine whether each pair of figures is similar. If so, write the similarity
statement and scale factor. If not, explain your reasoning.
3.
"
4.
)
#
1
+
(
&
4
-
22
5
1
PQR ∼ PST; scale factor −
no, ∠L ∠E
Chapter 7
3
11
,
$
%
2
2
12
Glencoe Geometry
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Exercises
NAME
DATE
7-2
PERIOD
Study Guide and Intervention (continued)
Similar Polygons
Use Similar Figures You can use scale factors and proportions to find missing side
lengths in similar polygons.
S
32
R
x
T
38
M
13
y
P
Use the congruent angles to write the
corresponding vertices in order.
RST ∼ MNP
Write proportions to find x and y.
32
x
38
32
−
−
=−
y =−
16
13
16
16x = 32(13)
x = 26
)
The scale factor is
N
16
Example 2
If DEF ∼ GHJ, find the
scale factor of DEF to GHJ and the
perimeter of each triangle.
32y = 38(16)
y = 19
&
8
EF
2
−
=−
=−
.
12
HJ
8
10
3
The perimeter of DEF
is 10 + 8 + 12 or 30.
%
12
+
'
12
Perimeter of DEF
2
−
= −−
(
Theorem 7.1
3
Perimeter of GHJ
30
2
−
=−
x
3
Substitution
(3)(30) = 2x
Cross Products Property
45 = x
Solve.
Lesson 7-2
Example 1
The two polygons are
similar. Find x and y.
So, the perimeter of GHJ is 45.
Exercises
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Each pair of polygons is similar. Find the value of x.
1.
2.
8
x
4.5
9
10
x
x=6
3.
18
12
x = 2.25
4.
18
x+1
36
x + 15
24
18
40
x = 15
30
x=9
20
5. If ABCD ∼ PQRS, find the scale factor
of ABCD to PQRS and the perimeter
of each polygon.
"
#
1
2
14
4
scale factor −
; perimeter ABCD = 68;
5
%
$
4
3
25
perimeter PQRS = 85;
Chapter 7
5
10
12
2.5
13
Glencoe Geometry