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7.2 Exploring Similar Polygons
Similar: • corresponding angles are congruent AND• measures of their corresponding sides are proportional.
AB
C
DE
M
L N
OP
Angles are ≅ Sides are proportional.
Pentagon ABCDE ~ Pentagon LMNOP
Proportional means the ratios of the corresponding sides are equal.
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AB
C
DE
M
L N
OP
Angles are ≅ Sides are proportional.
Pentagon ABCDE ~ Pentagon LMNOP
A≅ LB≅ MC≅ ND≅ OE≅ P
AB BC CD DE EALM MN NO OP PL = = = =
3
3
4
5
A
B
C)
)
15
20
25
D
E
F
)
)
Similarity Statement: ABC ~ DEF Symbol for similar
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Are these rectangles similar?
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126
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Example 1
5
I
J H60o
7
3
ABC ~ HJI
C
B
A
60oy
4.5 40o
y = ? m<H =?
Example 2
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Find the value of x and y.
A
B C
DE
F G
H
720 y10
13
18
x
ABCD ~ EFGHExample 3
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The ratio of two corresponding sides of similar polygons is called the scale factor.
*Reduce the ratios in the proportion to get the scale factor.
A
B C
D
10E
F G
H
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What is the scale factor of ABCD to EFGH?
Example 4
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These are similar. Find X.
Q
P S
RV
W
U
T
QR = 14QP = 6PS = 8SR = 6
VU = 20UT = XWT = 35WV = X
14
8
6
20
6 X
35
X
Example 5
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Polygon RSTUV is similar to ABCDEV
R
U
ST
A
ED
BC4
35
x
18
y + 2
a) Find the scale factor:
Example 6
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V
R
U
ST
A
ED
BC4
35
x
18
y + 2
Polygon RSTUV is similar to ABCDE
b) Find x and y
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** Scale drawings are the most popular "reallife" form of similar figures.**
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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?
Example 7
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