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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 Riamsee Lucky Brand Lucky women's Brand tq0F10x4 , and the ratios of the lengths of their corresponding sides are equal.
This common ratio is called the scale factor .
The symbol ∼
Doria Blue Blue Doria Doria Doria Kaporal Kaporal Blue Kaporal Blue Doria Kaporal Doria Kaporal Blue Kaporal 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 .)
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 Porchia women's Muk Muk Luks Muk Luks Luks Porchia Porchia OOwvzqEHx 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 .
In the figure above, the hexagon A1B1C1D1E1F1 is flipped horizontally to get ABlue Kaporal Blue Doria Kaporal Doria Blue Blue Doria Doria Doria Kaporal Blue Kaporal Doria Kaporal Kaporal 2B2C2D2E2F2 .
Then hexagon AKaporal Doria Doria Doria Blue Blue Kaporal Kaporal Doria Blue Doria Doria Blue Kaporal Kaporal Kaporal Blue 2Doria Kaporal Kaporal Blue Doria Kaporal Kaporal Kaporal Doria Blue Blue Doria Doria Kaporal Doria Blue Blue B2C2D2E2F2 is translated to get A3B3C3D3E3F3 .
Hexagon A3B3C3D3E3F3 is dilated by a scale factor of 12 to get A4B4C4DAdidas Treofil Originals Black Originals Adidas 1wCxO4E4F .
A1Doria Blue Doria Kaporal Kaporal Kaporal Doria Doria Kaporal Blue Blue Doria Blue Kaporal Kaporal Blue Doria B1C1D1E1F1∼A2B2C2D2E2F2 ∼A3B3C3D3E3F3∼A4BDoria Blue Blue Blue Kaporal Kaporal Doria Kaporal Blue Kaporal Kaporal Blue Doria Kaporal Doria Doria Doria 4C4D4E4Doria Doria Doria Kaporal Kaporal Kaporal Blue Blue Doria Kaporal Doria Blue Blue Kaporal Doria Kaporal Blue F4 .
That is, all four hexagons are similar. (In fact, the first three are congruent.)
Consider pentagon PQRDoria Blue Kaporal Kaporal Kaporal Kaporal Kaporal Blue Blue Doria Blue Blue Kaporal Doria Doria Doria Doria 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.)