Sec. 7 2 Similar Polygons

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Sec. 7 2Similar Polygons

• Objectives
• 1) To identify similar polygons
• 2) To apply similar polygons.

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Figures that are similar () have the same shape
but not necessarily the same size.
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All the angles are the same
All sides are proportional
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Similar Polygons 2 polygons that have the same
shape but not the same size.

• Symbol ( )
• Corresponding ?s are ?.
• Corresponding sides are Proportional.

Equal Ratios Reduce to the same fraction!!
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Ex Order Matters
Y

• ?ABC ?XYZ

78?
4
6
BC corresponds to YZ
B
42?
X
Z
8
10
Find AB
4
6

AB 15
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AB
A
C
4
8

AC 20
m?B m?C
78 60
10
AC
Find AC
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Example Identifying Similar Polygons
Determine whether the polygons are similar. If
so, write the similarity ratio and a similarity
statement.
rectangles ABCD and EFGH
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Example 3
A boxcar has the dimensions shown. A model of
the boxcar is 1.25 in. wide. Find the length of
the model to the nearest inch.
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Example 3 Continued
1.25(36.25) x(9)
Cross Products Prop.
45.3 9x
Simplify.
5 ? x
Divide both sides by 9.
The length of the model is approximately 5 inches.
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Ex. 2 Are the following polygons similar?
2in
B
C
1in
120?
K
L
1in
4in
4in
2in
2in
80?
J
M
1in
A
D
2in

• Check to see if all ?s are ??
• Check the ratio of all corresponding sides?

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Golden Rectangle Is a rectangle that can be
divided into a square and a rectangle that is
similar to the original rectangle.

• Pleasing to the eye.
• In Architecture since the Greeks.
• Da Vinci (1452 1519)
• Divine Proportion A book about the golden
  ratio.
• Golden Ratio 1.6181

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The golden rectangle R, constructed by the
Greeks, has the property that when a square is
removed a smaller rectangle of the same shape
remains. Thus a smaller square can be removed,
and so on, with a spiral pattern resulting.
                                                  
                                                  
                                                  
                               The Greeks were
thus able to see geometrically that the sides of
R have an irrational ratio, 1 x. The smaller
rectangle has sides with ratio 1-x 1 since
this is the same as the ratio for the big
rectangle, one finds that x2 x1 and thus x
(1Sqrt(5))/2 1.618033989....
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GOLDEN RATIO 1.618
The Golden Section is also known as the Golden
Mean, Golden Ratio and Divine Proportion.  It
is a ratio or proportion defined by the number
Phi (   1.618033988749895... ) It can be
derived with a number of geometric
constructions, each of which divides a line
segment at the unique point where the ratio of
the whole line (A) to the large segment (B) is
the same as the ratio of the large segment (B) to
the small segment (C).                          
                                                  
                   In other words, A is to B as B
is to C. This occurs only where A is 1.618 ...
times B and B is 1.618 ... times C.
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