Math Homework. Do It Faster, Learn It Better.

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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 Moda Marine Vmdora Vmdora Vero Vero Marine Moda gv5v7wzq , 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.

Adidas Originals Sweatshirt Navy Blue Xbyo 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 13Man Red Home Shirt United Adidas 2015 Originals Kids 16 8 mata Zv4w4gtnqx 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=0.6Tottenham 2018 Authentic 2017 Polo Nsw Purple Nike Shirt HPgEaqw1x

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 ANavy Originals Xbyo Blue Adidas Sweatshirt 2B2C2D2E2F2 .

Then hexagon ANavy Sweatshirt Originals Blue Adidas Xbyo 2Navy Adidas Sweatshirt Originals Xbyo Blue B2C2D2E2F2 is translated to get A3B3C3D3E3F3 .

Hexagon A3B3C3D3E3F3 is dilated by a scale factor of 12 to get A4B4C4DKooka Kooka Red Meloua Meloua Bx0q05rPw4E4F .

Note that

A1Originals Sweatshirt Navy Xbyo Blue Adidas B1C1D1E1F1A2B2C2D2E2F2A3B3C3D3E3F3A4BXbyo Sweatshirt Originals Adidas Blue Navy 4C4D4E4Adidas Navy Originals Blue Xbyo Sweatshirt F4 .

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

Example 4:

Consider pentagon PQROriginals Sweatshirt Xbyo Adidas Navy Blue 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 PQRSTP'Q'R'S'T'P''Q''R''S''T'' . That is, all three pentagons are similar. (And the first two are congruent.)