# Similar figures and geometric constructions

Similar figures are the same shape as each other, but
may be different sizes. The *scale factor* is the ratio between the sizes
of the two shapes. For instance, these two similar rectangles have a scale
factor of 2.0:

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The scale factor is the ratio between the lengths of
any *corresponding* sides. For instance, we could work the scale factor
out by comparing the top side lengths – one is 2.5 cm long, and one is 5 cm
long, twice as long. The scale factor *does not* correspond to the ratio
in the areas of the two shapes. These rectangles have a scale factor of 2, but
the ratio between their *areas *is 4.

In general, if you’re trying to work out the scale
factor, find two *corresponding* sides and work out the ratio in their
side lengths. You can’t use angles to work out a scale factor because the
angles don’t change between two similar figures, only the side lengths.

Say we didn’t know the length of the 5 cm side in the large rectangle. If we were told that the rectangles were similar, we could first work out the scale factor using the 1.5 cm and 3 cm sides. Then, we could multiply the 2.5 cm side on the small rectangle by the scale factor to work out the length of the unknown side in the large rectangle.

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