8.3 Similar Polygons
Essential Question:
How do you determine if two
polygons are similar?
Similar Polygons
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Polygons are similar if
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They are the same shape
Their corresponding angles are congruent
Their corresponding sides are proportional
Similarity Statements
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A similarity statement states the
similarity relationship of similar
polygons.
Example: ΔABC ∾ ΔDEF
The symbol for similarity is ∾.
Example: Decide whether the
figures are similar.
Example:

You have a 4 in. X 6 in. photo you would like
to use for class election posters. You want
the enlargement to be 26 inches wide. How
long will it be?
Example: JKLM is similar to
PQRS. Find the value of x.
Scale Factor
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If two polygons are similar, then the
ratio of the lengths of two
corresponding sides is called the scale
factor.
Example:
Theorem
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If two polygons are similar, then the
ratio of their perimeters is equal to the
ratios of their corresponding side
lengths.
Example:

The ratio of one side of ∆ABC to the
corresponding side of similar ∆DEF is
3:5. The perimeter of ∆DEF is 48
inches. What is the perimeter of ∆ABC?
Example:

The ratio of one side of ∆ABC to the
corresponding side of similar ∆DEF is
5:8. The perimeter of ∆DEF is 96
inches. What is the perimeter of ∆ABC?
Example:
ABCD and EFGH are parallelograms

The perimeter of ABCD is 60 cm. The
perimeter of EFGH is 15 cm. and ABCD
is similar to EFGH. The lengths of two
of the sides of ABCD are 18 cm. each.
Find the scale factor of ABCD to EFGH,
and the lengths of the sides of EFGH.
Polygon ABCD is similar to
polygon GHIJ.