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In
mathematics, polygons are similar
if their corresponding angles are congruent and the ratio
of their corresponding sides are in proportion. |
Once we know that triangles (or any
polygons) are similar, we also know some additional facts about the
figures.
| 1. Ratio of
Perimeters, Altitudes, Medians, Diagonals, and Angle Bisectors |
If two
polygons are similar, their corresponding sides, altitudes, medians,
diagonals, angle bisectors and
perimeters are all in the same ratio.
Example:
If the sides of two
similar triangles are in the ratio 4:9, what is the ratio of
their perimeters?
Answer:
4:9 |
If two polygons
are similar, the ratio of their areas is equal to the square
of the ratio of their corresponding sides.
Example:
If the sides of two
similar triangles are in the ratio of 3:5, find the ratio of
their areas.
Answer:
9:25
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If two polygons
are similar, the ratio of their volumes
is equal to the cube
of the ratio of their corresponding sides.
Example:
If the sides of two
similar triangles are in the ratio of 2:3, find the ratio of
their volumes.
Answer:
8:27
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