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Similar Polygons & Scale Factor
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Similar Polygons 1. Corresponding angles are congruent
2. Corresponding sides are proportional
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Similarity Statement ABC ~ DEF
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Solve for x and y. x = 26 cm y = 12 cm L A 5 cm x S 10 cm y 13 cm C B
T x = 26 cm y = 12 cm
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ABCD ~ EFGH. Solve for x. G H D C x 27 A B 6 F E 18 x = 9
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Ex. A tree cast a shadow 18 feet long
Ex. A tree cast a shadow 18 feet long. At the same time a person who is 6 feet tall cast a shadow 4 feet long. How tall is the tree?
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Ratio of Similar Polygons
12/30/2018 Ratio of Similar Polygons Corresponding Sides : Corresponding Sides Or Perimeter : Perimeter A : B
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Ratio of Similar Polygons
12/30/2018 Ratio of Similar Polygons Area : Area A2 : B2
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Ratio of Similar Polygons
12/30/2018 Ratio of Similar Polygons Volume: Volume A3 : B3
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The ratio of the perimeters of two similar polygons equals the ratio of any pair of corresponding sides. The ratio of the perimeters of CAT to DOG is 3:2 Find the value of y. A C T O D G 4 10 y y = 4
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Find the perimeter of the smaller triangle.
12 cm 4 cm Perimeter = x Perimeter = 60 cm x = 20 cm
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Scale Factor – the ratio of a new image to its original image
The ratio of corresponding sides
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Scale Factor When scale factor is greater than 1, the shape gets bigger (enlargement). When scale factor is less than 1, but greater than 0, the shape gets smaller (reduction).
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SCALE FACTOR. 6 2 new original 7 14 10 5 original new 3 6
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All you do is multiply k to (x, y).
Find the coordinates of the dilation image for the given scale factor, k. Example 1: G(0, -2), H(1, 3), and I(4, 1); k = 2 All you do is multiply k to (x, y). G’( , ), H’( , ), and I’( , ) 0 -4 2 6 8 2
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All you do is multiply k to (x, y).
Find the coordinates of the dilation image for the given scale factor, k. Example 2: L(8, -8), N(0, 16), and M(4, 5); k = 1/4 All you do is multiply k to (x, y). L’( , ), N’( , ), and M’( , ) 2 -2 0 4 1 5/4
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k = 1/2
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k = 2
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Worksheet
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