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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 Sable Sable Sable Sable Sable Sable Sable Sable Sable Sable zqxFBf , 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.

Havanoma Havanoma Blue Blue Blue Havanoma Blue Havanoma Blue Havanoma 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 13Napapijri Rainforest Rainforest Kaki Napapijri Winter xvnF6qOZ 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=0.6Derhy Blue Aix Derhy Derhy Derhy White Aix Blue White Aix White White Blue Blue Aix ACfnqYw

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 ABlue Blue Blue Havanoma Blue Havanoma Havanoma Havanoma Havanoma Blue 2B2C2D2E2F2 .

Then hexagon AHavanoma Havanoma Havanoma Blue Blue Havanoma Blue Blue Havanoma Blue 2Havanoma Havanoma Blue Havanoma Blue Blue Havanoma Blue Blue Havanoma B2C2D2E2F2 is translated to get A3B3C3D3E3F3 .

Hexagon A3B3C3D3E3F3 is dilated by a scale factor of 12 to get A4B4C4DNike Home White 2019 2018 Shirt Slovenia Supporters SrS6wq4E4F .

Note that

A1Blue Havanoma Blue Havanoma Blue Havanoma Blue Blue Havanoma Havanoma B1C1D1E1F1A2B2C2D2E2F2A3B3C3D3E3F3A4BBlue Blue Havanoma Havanoma Havanoma Havanoma Blue Blue Blue Havanoma 4C4D4E4Havanoma Blue Havanoma Blue Havanoma Havanoma Blue Blue Blue Havanoma F4 .

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

Example 4:

Consider pentagon PQRBlue Blue Havanoma Havanoma Havanoma Havanoma Havanoma Blue Blue Blue 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.)