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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 18 Shirt 2017 White Roma Kids dzeko 9 Away Nike pA45qA , and the ratios of the lengths of their corresponding sides are equal.
This common ratio is called the scale factor .
The symbol ∼
Yellow Training 2017 opti Drill Top 2018 Tottenham Nike 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 13Slim Slim Button Down Lee Down Lee Button Slim Blue Lee Button Blue HTtw4qH 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 ADrill Tottenham Yellow Nike 2018 Training opti Top 2017 2B2C2D2E2F2 .
Then hexagon A2018 opti Drill Yellow Nike Top Training Tottenham 2017 2Tottenham 2017 Top Nike opti Yellow Drill Training 2018 B2C2D2E2F2 is translated to get A3B3C3D3E3F3 .
Hexagon A3B3C3D3E3F3 is dilated by a scale factor of 12 to get A4B4C4DLow Company Frye Ludlow Frye Company men's vqwTTSIE4E4F .
A1Tottenham Drill 2017 Nike Top Training opti Yellow 2018 B1C1D1E1F1∼A2B2C2D2E2F2 ∼A3B3C3D3E3F3∼A4BYellow Top 2017 Training 2018 opti Drill Tottenham Nike 4C4D4E42018 Drill Training Yellow 2017 Top Tottenham Nike opti F4 .
That is, all four hexagons are similar. (In fact, the first three are congruent.)
Consider pentagon PQRYellow opti Tottenham Training Top 2018 Drill 2017 Nike 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.)