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7-2 Similar Polygons

7-2 Similar Polygons. Similarity. Similar figures have the same shape but not necessarily the same size. The ~ symbol means “is similar to”

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7-2 Similar Polygons

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  1. 7-2 Similar Polygons

  2. Similarity • Similar figures have the same shape but not necessarily the same size. • The ~ symbol means “is similar to” • Two polygons are similar polygons if corresponding angles are congruent and if the lengths of corresponding sides are proportional. • When three or more ratios are equal, you can write an extended proportion.

  3. Understanding Similarity MNP ~ SRT • What are the pairs of congruent angles? • What is the extended proportion for the ratios of corresponding sides?

  4. DEFG ~ HJKL • What are the pairs of congruent angles? • What is the extended proportion for the ratios of the lengths of corresponding sides?

  5. Scale Factor • A scale factor is the ratio of corresponding linear measurements of two similar figures. • The ratio of corresponding sides is , so the scale factor of ABC to XYZ is or 5 : 2.

  6. Determining Similarity • Are the polygons similar? If they are, write a similarity statement and give the scale factor.

  7.  Are the polygons similar? If they are, write a similarity statement and give the scale factor.

  8. Using Similar Polygons • ABCD ~ EFGD. What is the value of x?  What is the value of y?

  9. Using Similarity • In the diagram, Find SR.

  10.  In the diagram, Find CE.

  11. Scales • In a scale drawing, all lengths are proportional to their corresponding actual lengths. • The scale is the ratio that compares each length in the scale drawing to the actual length. • The lengths used in a scale can be in different units (ex. 1 cm = 50 km). • You can use proportions to find the actual dimensions represented in a scale drawing.

  12. Using a Scale Drawing • The diagram shows a scale drawing of the Golden Gate Bridge. If the length between the two towers in the diagram is 6.4 cm, what is the length of the actual bridge? If the tower measures 0.8 cm in the diagram, what is the actual height of the tower?

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