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Warm Up The geometric mean of 12 and another number is 30. What is the other number?
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Similar Polygons Geometry
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SIMILAR POLYGONS Two polygons such that their corresponding angles are congruent and the lengths of corresponding sides are proportional. The symbol for “is similar to” is ~
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2 Statements We Need to Know
Similarity Statement Simply write that the figures are similar Be sure to list the corresponding angles in the same order Statement of Proportionality We write all the corresponding sides as a proportion
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Similar Polygons
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Example Trapezoid ABCD is similar to trapezoid PQRS. List all the pairs of congruent angles, and write the ratios of the corresponding sides in a statement of proportionality.
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Similar Polygons COMET ~ HAIRY Which angles are congruent? Write the ratios of the corresponding sides in a statement of proportionality.
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Are the polygons similar?
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To Check if the polygons are similar
Are the corresponding angles congruent? Are the corresponding side lengths proportional? (reduce all ratios to see if they are equal)
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Are the polygons similar?
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Example You have a photo 4 in. wide by 6 in. long that you want to reduce to fit in a frame that is 1.5 in. wide. How long will the reduced photo be?
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Example ▲UVW is similar to ▲YXW. Find the value of a. U V a 5 W 6.4 12
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SCALE FACTOR If two polygons are similar, then the ratio of the lengths of two corresponding sides is called the scale factor. To find the scale factor, find the reduced common ratio.
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Example A painting is similar to the wall on which it is hanging. Calculate the scale factor of the wall to the painting and find the ratio of their perimeters. 15 ft 3.2 ft 8 ft 6 ft
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Similar Polygons and their Perimeters
If two polygons are similar, then the ratio of their perimeters is equal to the ratios of their corresponding side lengths.
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Example If ABCDE ~ PQRST, find the scale factor of ABCDE to PQRST and the perimeter of each polygon.
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Example In the diagram, ACDF ~ VWYZ. Find x and y. A C 10 Y Z 12 9 6
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