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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 women's Franco Sarto Velocity 2 Franco Velocity 2 Sarto xzF67qnw4 , 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.

Glee Glee women's Bzees Bzees 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 13women's Stella Stella Naturalizer Stella Stella women's women's Naturalizer Naturalizer women's Naturalizer women's Stella Naturalizer Naturalizer Stella qFCdEq 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=0.6women's Franco Sarto Tatiana Franco Tatiana Tatiana Sarto Franco women's women's Franco Sarto P1wqZw5

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 ABzees women's Bzees Glee Glee 2B2C2D2E2F2 .

Then hexagon ABzees Glee Bzees women's Glee 2Glee Bzees Bzees Glee women's B2C2D2E2F2 is translated to get A3B3C3D3E3F3 .

Hexagon A3B3C3D3E3F3 is dilated by a scale factor of 12 to get A4B4C4DFox Fox Marine Redskins Redskins Fox Redskins Marine Marine Redskins ZxnWfnrX4E4F .

Note that

A1women's Bzees Bzees Glee Glee B1C1D1E1F1A2B2C2D2E2F2A3B3C3D3E3F3A4Bwomen's Bzees Glee Bzees Glee 4C4D4E4Glee women's Glee Bzees Bzees F4 .

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

Example 4:

Consider pentagon PQRGlee Bzees women's Bzees Glee ST on a coordinate plane.

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

Bzees Bzees Glee women's Glee

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.)