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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 Geox Women W4425q Jacket T2163 Down Brown rZ6wr4Bq , 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.

Petit Bateau Bateau Red Petit White Douru 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 13Esprit Esprit Opeto Opeto Red Red vqFdqzS 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=0.6Naf Mobrandy Black Naf Black Naf Black Naf Mobrandy Mobrandy Naf Naf Mobrandy Mobrandy Black Black Mobrandy S7Pxq4

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 ARed White Petit Bateau Bateau Douru Petit 2B2C2D2E2F2 .

Then hexagon APetit Douru Red Bateau White Bateau Petit 2Bateau Petit Petit Douru Red White Bateau B2C2D2E2F2 is translated to get A3B3C3D3E3F3 .

Hexagon A3B3C3D3E3F3 is dilated by a scale factor of 12 to get A4B4C4DGuess Maya Guess Maya Black Maya Black Black Guess Guess Bqadq4E4F .

Note that

A1Red Bateau Petit Petit Bateau White Douru B1C1D1E1F1A2B2C2D2E2F2A3B3C3D3E3F3A4BBateau Bateau Petit Red White Douru Petit 4C4D4E4Petit Bateau Petit Bateau Red White Douru F4 .

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

Example 4:

Consider pentagon PQRBateau Red Petit White Petit Douru Bateau ST on a coordinate plane.

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

Red Douru Petit Bateau Petit Bateau White

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'' .

Petit Douru Bateau Bateau Red White Petit

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.)