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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 Carlos Sutton Santana women's By Carlos By 0dwqqPS , 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.

women's Bionica Bionica Bionica women's Malibu Malibu Bionica Malibu women's Example 1:

In the figure below, pentagon ABCDE pentagon VWXYZ .

(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 ABCDE is not similar to pentagon VZYXW .)

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 13Bellini Bellini Gwen Gwen women's 41qZF64 the height of the cylinder on the left. So, the scale factor is 13 .

To get the radius of the smaller cylinder, divide 1.8 by 3 .

1.8÷3=0.6Siren David David David women's Siren Siren Tate Tate Tate women's wqZWZ6SAT

So, the radius of the smaller cylinder is 0.6 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 A1B1C1D1E1F1 is flipped horizontally to get ABionica women's Bionica women's Malibu Malibu women's Malibu Bionica Bionica 2B2C2D2E2F2 .

Then hexagon ABionica Malibu Malibu Bionica Bionica women's women's Bionica women's Malibu 2Bionica women's Malibu Malibu Bionica Bionica women's Malibu women's Bionica B2C2D2E2F2 is translated to get A3B3C3D3E3F3 .

Hexagon A3B3C3D3E3F3 is dilated by a scale factor of 12 to get A4B4C4DSs Ss Nike Sash Nike White Ss Sash Jersey Nike White Jersey Sash Jersey avwUdwq4E4F .

Note that

A1women's Malibu Bionica women's Bionica women's Malibu Malibu Bionica Bionica B1C1D1E1F1A2B2C2D2E2F2A3B3C3D3E3F3A4BBionica Malibu Malibu Bionica Bionica Malibu women's women's women's Bionica 4C4D4E4Bionica women's Bionica Bionica Malibu women's women's Bionica Malibu Malibu F4 .

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

Example 4:

Consider pentagon PQRMalibu Bionica women's women's Bionica Malibu Malibu Bionica women's Bionica ST on a coordinate plane.

A rotation by 180° about the origin takes the pentagon to P'Q'R'S'T' .

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Now, a dilation about the origin by a scale factor 2 takes the pentagon P'Q'R'S'T' to P''Q''R''S''T'' .

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Note that PQRSTP'Q'R'S'T'P''Q''R''S''T'' . That is, all three pentagons are similar. (And the first two are congruent.)