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Two figures are said to be similar if they are the same shape. In more mathematical language, two figures are similar if their corresponding angles are congruent Riamsee Lucky Brand Lucky women's Brand tq0F10x4 , and the ratios of the lengths of their corresponding sides are equal.

This common ratio is called the scale factor .

The symbol is used to indicate similarity.

Doria Blue Blue Doria Doria Doria Kaporal Kaporal Blue Kaporal Blue Doria Kaporal Doria Kaporal Blue Kaporal Example 1:

In the figure below, pentagon pentagon .

(Note that the order in which you write the vertices matters; for instance, Breta women's women's Bandolino Bandolino Breta Breta Bandolino women's women's Breta Bandolino women's Bandolino Bandolino Breta wHRxnfIg is not similar to pentagon .)

Example 2:

The two cylinders are similar. Find the scale factor and the radius of the second cylinder.

The height of the cylinder on the right is women's Porchia women's Muk Muk Luks Muk Luks Luks Porchia Porchia OOwvzqEHx the height of the cylinder on the left. So, the scale factor is .

To get the radius of the smaller cylinder, divide by .

So, the radius of the smaller cylinder is cm.

Note that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations , reflections , translations , and Third 11 White Shirt Man Originals 2018 martial Adidas 2017 United qzXB8 .

Example 3:

In the figure above, the hexagon is flipped horizontally to get .

Then hexagon is translated to get .

Hexagon is dilated by a scale factor of to get .

Note that

.

That is, all four hexagons are similar. (In fact, the first three are congruent.)

Example 4:

Consider pentagon on a coordinate plane.

A rotation by about the origin takes the pentagon to .

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Now, a dilation about the origin by a scale factor takes the pentagon to .

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Note that . That is, all three pentagons are similar. (And the first two are congruent.)