Similar Polygons

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Similar Polygons
J Pavlicek (2005) Edited J Stoops (2007)
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Objectives

• Identify similar polygons
• Use similar polygons to solve real-life problems

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Def Two polygons are similar if they have the
same shape.
If two polygons are similar, then their vertices
can be paired such that . . . 1.) corresponding
angles are congruent 2.) corresponding sides
are proportional
B
X
ABCD ? WXYZ
A
W
Y
Z
C
D
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B
X
A
W
Similarity Statement
ABCD ? WXYZ
Y
Z
C
D
Proportionality Statement

• A ? ? W
• B ? ? X
• C ? ? Y
• D ? ? Z

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Example Determine whether the following
polygons are similar.
G
S
14 cm
7 cm
4 cm
8 cm
H
F
10 cm
T
R
20 cm
1.) Are corresponding angles congruent?
2.) Are corresponding sides proportional?
Similarity Statement ?
Def The scale factor of similar polygons is the
ratio of any pair of corresponding sides.
Example What is the scale factor of the above
similar triangles?
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Parallelogram ABCD ? Parallelogram GBEF
Example
B E C
60?
12
x?
y
G F
15
A D
24
1.) What is the scale factor of ABCD to GBEF?
2.) Find the values of x and y.
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Theorem If two polygons are similar, then the
ratio of their perimeters is equal to
the scale factor.
Suppose the following are similar. Prove the
above theorem.
b
s
r
t
a
c
u
d
NOTE If two polygons are similar, then the
ratio of ANY corresponding lengths is equal to
the scale factor.
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Example Quad ABCD ? JKLM. Complete each of the
following.
A
J
12t
28
K
1.) m?M ______ 2.) m?C ______
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B
M
L
15
70?
C
D
20
3.) The scale factor of JKLM to ABCD is
_____ 4.) BC ______ 5.) JM ______ 6.)
JK ______ 7.) The ratio of the perimeter of
ABCD to the perimeter of JKLM ______
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Tell whether the two polygons are sometimes,
always, or never similar.
1.) Two equilateral triangles. 2.) Two
isosceles triangles. 3.) Two squares 4.) Two
scalene triangles. 5.) Two rhombuses. 6.) A
right triangle and an acute triangle. 7.) Two
regular polygons. 8.) An isosceles triangle and
a scalene triangle. 9.) A right triangle and a
scalene triangle. 10.) Trapezoid and a rhombus.
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Assignment pg 476 19 42 Quiz tomorrow over
Sections 8.1 and 8.2