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Figures that
have the same shape,
but do not have the same size,
are said to be
similar.
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These two
photographs of Sadie are the same shape, but they are
not the same size.
The photographs are called
similar figures. |
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Similar
Symbol
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In
mathematics, figures are said to be similar if
their corresponding
angles are equal and their corresponding
sides are in proportion. |
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The ratio of the
corresponding sides of similar figures is called the
ratio of similitude.
This ratio of similitude is also the ratio of the
corresponding diagonals, altitudes, medians, angle bisectors,
apothems and perimeters. |
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Remember
- when working with triangles,
triangles are similar when two pairs of corresponding
angles are congruent.
(AA) |
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These are two
regular pentagons.
(A regular polygon has all of its sides
equal and all of its angles equal.)
The
pentagons are similar. Their ratio
of similitude is 8 : 4
(reduced 2 : 1). |
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Example:
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These
two rhombi are similar. Their
ratio
of similitude
is 3 : 1.
Find x.
Solution:
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3x
= 12
x = 4 |
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Example:
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Rectangle ABCD is
similar to rectangle A'B'C'D' where A corresponds to A' and so
on.
If AB = 12, A'B' = 4, AD = 9, find A'D'.
Solution:
Establish a proportion by pairing the corresponding sides.
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12x = 36, x = 3
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