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Similar Figures
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Similar Figures
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Students
should be able to:
use proportional reasoning
to describe and express relationships between parts and attributes
of similar figures.
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Introduction
to Similar Figures
Similar figures have the same
shape but not the same size.
The corresponding angles are
congruent and corresponding sides are in proportion. This
means that you can that you can make a proportion (an equation
that states that two ratios are equal) out of the corresponding
sides. The ratio of the corresponding sides is called the
ratio of similtude.
Ratios are written three ways:
a:b, a/b, a to b
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Example
1
The
left side of the L below has a length of 2.
Press the orange button to create a congruent L
that will grow to be a similar L. Its left side
will have a length of 4. The ratio of
similitude will be 2:4. |
| The
symbol for similar is
~
We put this symbol between
two shapes that are the similar to each other. For instance,
to show that the two L's above are similar, we would write
L#1
~ L#2
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Example 2
The
left side of the T below has a length of 2.
Press the blue button to create a congruent T that
will grow to be a similar T. Its left side
will have a length of 6. The ratio
of similitude will be 2:6. |
Example 3
Notice
that the T's below are congruent. When you click the button,
the T on the right will shrink so that the T's will be similar.
The T's will be in proportion. |
The sides
are in proportion. From top to bottom:
9:3,
3:1, 6:2
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