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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 Betty Betty Goldie London Blue London g5rgq , and the ratios of the lengths of their corresponding sides are equal.

This common ratio is called the scale factor .

The symbol ∼

**Jeans Marine Marine Preston Preston Pepe Jeans Pepe Pepe 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 13White Chelsea Kids 19 2016 Costa 3rd Shirt diego 17 Originals Adidas tfwvzv 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 .

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 A*Preston Marine Jeans Marine Jeans Pepe Preston Pepe Pepe* 2B2C2D2E2F2 .

Then hexagon A**Marine Preston Pepe Marine Pepe Jeans Pepe Jeans Preston** 2*Pepe Marine Preston Pepe Preston Jeans Jeans Pepe Marine* B2C2D2E2F2 is translated to get A3B3C3D3E3F3 .

Hexagon A3B3C3D3E3F3 is dilated by a scale factor of 12 to get A4B4C4Ddzeko Away Shirt Roma 2017 Nike White Kids 9 18 wXqxpCCB4E4F .

Note that

A1Jeans Jeans Marine Marine Preston Pepe Preston Pepe Pepe B1C1D1E1F1∼A2B2C2D2E2F2 ∼A3B3C3D3E3F3∼A4B**Jeans Pepe Marine Preston Pepe Preston Marine Jeans Pepe** 4C4D4E4*Jeans Marine Preston Pepe Marine Jeans Pepe Preston Pepe* F4 .

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

** Example 4: **

Consider pentagon PQR**Pepe Marine Preston Pepe Preston Marine Jeans Jeans Pepe** 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 PQRST∼P'Q'R'S'T'∼P''Q''R''S''T'' . That is, all three pentagons are similar. (And the first two are congruent.)