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### Understanding Similar Polygons and Scale Factors in Geometry ###

This guide explores the concept of similar polygons, which share the same shape but may differ in size. It defines the necessary conditions for similarity, including congruent angles and proportional sides, illustrated through examples of triangles and quadrilaterals. The scale factor is introduced as the ratio of corresponding side lengths. Additionally, the guide provides methods for determining similarity, formulating similarity statements, finding missing side lengths using proportions, and applying scale drawings to real-life measurements. ###

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### Understanding Similar Polygons and Scale Factors in Geometry ###

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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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