7.2 Exploring Similar Polygons
Proportional means the ratios of the corresponding sides are equal.
Similar:
• corresponding angles are congruent AND
• measures of their corresponding sides are proportional.
M
B
A
C
E
N
L
D
Pentagon ABCDE ~ Pentagon LMNOP
Angles are ≅
P
O
Sides are proportional.
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Pentagon ABCDE ~ Pentagon LMNOP
M
B
A
C
E
N
L
D
P
Angles are ≅
A≅ L
B≅ M
C≅ N
D≅ O
E≅ P
O
Sides are proportional.
AB BC CD DE EA
=
=
=
=
LM MN NO OP PL 2
Similarity Statement:
ABC ~ DEF
Symbol for similar
E
B
­
)
­
)
5
3
A
­­
4
15
)
C
D
25
)
­­
20
F
3
Example 1
Are these rectangles similar?
8
12
6
7
4
Example 2
B
o
60
4.5
y
40o
A
y = ?
I
ABC ~ HJI
7
C
o
60
J
3
H
m<H =?
5
Example 3
ABCD ~ EFGH
Find the value of x and y.
B
0
72
10
A
13
C
G
F
18
y
D
E
x
H
6
The ratio of two corresponding sides of
similar polygons is called the scale factor.
Example 4B
C
F
5
10
A
G
E
H
D
What is the scale factor of ABCD to EFGH?
*Reduce the ratios in the proportion to get the scale factor.
7
Example 5
These are similar. Find X.
14
Q
V
R
6
8
S
W
U
QR = 14
QP = 6
PS = 8
SR = 6
X
X
6
P
20
35
T
VU = 20
UT = X
WT = 35
WV = X
8
Example 6
Polygon RSTUV is similar to ABCDE
V
x
E
U
R
y + 2
S
18
T
D
3
5
A
B 4
C
a) Find the scale factor:
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Polygon RSTUV is similar to ABCDE
V
x
E
U
R
y + 2
S
18
T
D
3
5
A
B 4
C
b) Find x and y
10
** Scale drawings are the most popular "real­life" form of similar figures.**
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Example 7
Delaware is a very small state, shaped similarly to a five­sided polygon. The scale on a map of Delaware is approximately 2cm = 50 miles. The distance on the map across Delaware from east to west is 1.4 cm. How many miles is it to drive across Delaware if you drove 50 mph?
How long would it take?
12
13
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