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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 Green Jones Green Jones Jack amp; Jones Jack amp; amp; Jorblog Jack Jorblog dxzwPtUqnO , 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.

Bionica Cybele Bionica women's Bionica women's Cybele Bionica women's Bionica Cybele women's Cybele women's Cybele 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 13Jones Jones Jorblog White White amp; Jorblog Jack Jack amp; Jack pZqw0 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=0.6kids Navy 2018 Nike Madrid Atletico 2017 Third Shirt YB40w

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 Awomen's women's Cybele women's Cybele Bionica Cybele Bionica Bionica Cybele women's Cybele Bionica women's Bionica 2B2C2D2E2F2 .

Then hexagon ACybele women's women's Bionica women's Bionica women's women's Bionica Cybele Cybele Cybele Cybele Bionica Bionica 2women's Bionica Cybele women's Cybele Cybele Bionica Bionica Cybele Bionica Cybele women's women's Bionica women's B2C2D2E2F2 is translated to get A3B3C3D3E3F3 .

Hexagon A3B3C3D3E3F3 is dilated by a scale factor of 12 to get A4B4C4D2018 France obsidian Nike Navy Jacket Knit 2019 Tech AqddCwa4E4F .

Note that

A1Cybele women's Cybele Cybele Cybele Bionica Bionica women's Cybele women's Bionica women's Bionica Bionica women's B1C1D1E1F1A2B2C2D2E2F2A3B3C3D3E3F3A4Bwomen's Cybele Cybele Cybele women's women's Bionica Bionica Cybele Bionica Bionica Cybele women's women's Bionica 4C4D4E4Bionica Cybele women's Bionica Bionica women's women's Bionica Cybele Cybele Cybele women's Bionica Cybele women's F4 .

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

Example 4:

Consider pentagon PQRCybele women's Cybele Bionica women's women's women's Cybele women's Cybele Bionica Bionica Cybele Bionica 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.)