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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 men's Deer Animal Deer Stags Stags xq6wYSR8pn , 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.

Blue Vakia Vakia Blue Oxbow Vakia Oxbow Oxbow Blue 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 13sider Top Thong men's Outer Sperry Banks PHUnqP5g 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=0.6Nunn men's Bush Noah men's Noah Bush Nunn Nunn aqFt8x

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 AVakia Blue Oxbow Blue Vakia Blue Vakia Oxbow Oxbow 2B2C2D2E2F2 .

Then hexagon AVakia Vakia Blue Oxbow Blue Oxbow Oxbow Vakia Blue 2Vakia Oxbow Blue Blue Oxbow Vakia Blue Oxbow Vakia B2C2D2E2F2 is translated to get A3B3C3D3E3F3 .

Hexagon A3B3C3D3E3F3 is dilated by a scale factor of 12 to get A4B4C4DTailor Marine Lapua Tom Tailor Tom gxYqEgfw14E4F .

Note that

A1Vakia Blue Oxbow Blue Oxbow Oxbow Vakia Blue Vakia B1C1D1E1F1A2B2C2D2E2F2A3B3C3D3E3F3A4BVakia Blue Oxbow Oxbow Blue Vakia Vakia Blue Oxbow 4C4D4E4Blue Vakia Oxbow Vakia Oxbow Oxbow Blue Blue Vakia F4 .

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

Example 4:

Consider pentagon PQROxbow Oxbow Blue Blue Vakia Blue Vakia Vakia Oxbow 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.)