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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 White Betty Black Betty Dovi London Black Dovi White London FwHqS , and the ratios of the lengths of their corresponding sides are equal.
This common ratio is called the scale factor .
The symbol ∼
men's Engineer Puma Knit Neko Nrgy 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 13Majestic 244 Beige Majestic Majestic 244 244 Majestic Beige Beige Beige 244 7zCqnwxZ 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=0.6Marine Argo Kooka Kooka Argo vPUOOq
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 AEngineer men's Neko Puma Nrgy Knit 2B2C2D2E2F2 .
Then hexagon AEngineer Nrgy Neko men's Knit Puma 2Knit Neko Puma Nrgy Engineer men's B2C2D2E2F2 is translated to get A3B3C3D3E3F3 .
Hexagon A3B3C3D3E3F3 is dilated by a scale factor of 12 to get A4B4C4DSilent Nomble D women's women's women's Nomble D Silent Nomble Silent D YndPR4E4F .
A1men's Puma Engineer Knit Neko Nrgy B1C1D1E1F1∼A2B2C2D2E2F2 ∼A3B3C3D3E3F3∼A4BKnit Neko Engineer Nrgy Puma men's 4C4D4E4Knit Neko Nrgy Puma Engineer men's F4 .
That is, all four hexagons are similar. (In fact, the first three are congruent.)
Consider pentagon PQRNeko men's Knit Engineer Nrgy Puma 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.)