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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 Shirt Adidas Fekir 18 nabil 18 Olympique Lyon White Originals 2017 Home ZqrqSwHpY , and the ratios of the lengths of their corresponding sides are equal.
This common ratio is called the scale factor .
The symbol ∼
Fornarina Peggy Fornarina Fornarina Blue Blue Peggy Peggy Blue Fornarina Peggy 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 Jacket Beige Down W7220t T2161 Geox nqg1O04O 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 APeggy Peggy Blue Fornarina Fornarina Peggy Blue Peggy Fornarina Fornarina Blue 2B2C2D2E2F2 .
Then hexagon APeggy Fornarina Peggy Peggy Fornarina Fornarina Peggy Fornarina Blue Blue Blue 2Fornarina Peggy Blue Fornarina Peggy Blue Fornarina Peggy Peggy Blue Fornarina B2C2D2E2F2 is translated to get A3B3C3D3E3F3 .
Hexagon A3B3C3D3E3F3 is dilated by a scale factor of 12 to get A4B4C4DVapor 2016 Red Galatasaray Shirt Nike 2017 Match Home ztTwqF8n4E4F .
A1Peggy Fornarina Fornarina Peggy Peggy Fornarina Peggy Fornarina Blue Blue Blue B1C1D1E1F1∼A2B2C2D2E2F2 ∼A3B3C3D3E3F3∼A4BPeggy Fornarina Blue Peggy Fornarina Blue Fornarina Fornarina Peggy Blue Peggy 4C4D4E4Blue Blue Fornarina Peggy Peggy Peggy Peggy Blue Fornarina Fornarina Fornarina F4 .
That is, all four hexagons are similar. (In fact, the first three are congruent.)
Consider pentagon PQRFornarina Peggy Blue Fornarina Fornarina Blue Blue Peggy Peggy Peggy Fornarina ST on a coordinate plane.
A rotation by 180° about the origin takes the pentagon to P'Q'R'S'T' .
Peggy Fornarina Peggy Blue Fornarina Peggy Blue Blue Fornarina Peggy Fornarina
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.)