7.3 Similar Polygons

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7.3 Similar Polygons
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• If we were to draw a map of the united states, we
  would not take a roll of paper that is as big as
  the US to do it. We would take a smaller piece
  of paper and draw everything to scale. Therefore
  our map would be similar to the actual thing.
• Look at pg. 248 and realize why those stamps are
  similar.

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Similar ? same shape, different size

• Two polygons are similar if their vertices can be
  paired so that
• (1) Corresponding angles are congruent
• (2) Corresponding sides are in proportion
• (lengths have the same ratio)

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• When talking about two figures being similar we
  can make similarity statements much like we can
  make congruency statements. When we make
  similarity statements the order of our vertices
  still matters.

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B
If these polygons are similar, you would write
polygon VWXYZ polygon DEABC
What vertices match up to what vertices? Sides to
sides?
(1) (2)
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• If 2 polygons are similar, then the ratio of the
  2 corresponding sides is called the scale factor
  of the similarity.

B
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The scale factor of pentagon VWXYZ to pentagon
DEABC is
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• When finding the scale factor for 2 similar
  polygons, the scale factor depends on the order
  of comparison.

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• A more convenient way of labeling corresponding
  vertices is to use an apostrophe like mark. A
  and A, B and B, C and C (read A prime, B
  prime, C prime).
• Quad ABCD Quad ABCD

C
B
B
C
D
D
A
A
10
C
30
B
B
C
20
Quad ABCD Quad ABCD
y
10
8
z
D
D
A
x
A
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Find the scale factor Find values of x, y, and
z Find perimeters of both figures Identify
ratio of the perimeters
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Use the scale factor, or write proportions
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6.4 cm