Similar Polygons

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Lesson 7-2

• Similar Polygons

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Similar Polygons
Definition Two polygons are similar if 1.
Corresponding angles are congruent. 2.
Corresponding sides are in proportion.
Two polygons are similar if they have the same
shape not necessarily have the same size.
The scale factor is the ratio between a pair of
corresponding sides.
Scale Factor
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Like Dr. Evil and Mini Me
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Naming Similar Polygons
When naming similar polygons, the vertices
(angles, sides) must be named in the
corresponding order.
P
Q
A
B
C
D
S
R
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Example-
The two polygons are similar. Solve for x, y and
z.
Step1 Write the proportion of the sides.
Step 2 Replace the proportion with values.
Step 3 Find the scale factor between the two
polygons.
Note The scale factor has the larger
quadrilateral in the numerator and the smaller
quadrilateral in the denominator.
Step 4 Write separate proportions for each
missing side and solve.
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Example
If ?ABC ?ZYX, find the scale factor from ?ABC
to ?ZYX.
Scale factor is same as the ratio of the sides.
Always put the first polygon mentioned in the
numerator.
The scale factor from ?ABC to ?ZYX is 2/1.
½
What is the scale factor from ?ZYX to ?ABC?
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Example
V
U
E
D
3
x
A
5
R
y2
B
C
4
T
S
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Find the scale factor of polygon RSTUV to polygon
ABCDE
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Example

• Rectangle QRST is similar to rectangle JKLM with
  a scale factor of .8. If the lengths of the
  sides of rectangle JKLM are 5cm and 12 cm, what
  are the lengths of the sides of rectangle QRST?

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Example
Delaware is a very small state, shaped similarly
to a five-sided polygon. The scale on a map of
Delaware is approximately 2 centimeters50 miles.
The distance on the map across Delaware from east
to west is 1.4 centimeters. How long would it
take to drive across Delaware if you drove at
approximately 50 miles per hour?
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Example
Find x and y.
29
x
20
49
21
y 3
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Example
For each statement write always true, sometimes
true, or never true.
A) Two right triangles are similar.
B) Two congruent quadrilaterals are similar.
C) Two rectangles are similar.
D) A triangle is similar to a quadrilateral