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Chapter 7: Similarity

Chapter 7: Similarity. Section 7-2: Similar Polygons. Objectives. To identify similar polygons. To apply similar polygons. Vocabulary. Similar Similarity Ratio Golden Rectangle Golden Ratio. Similar Figures.

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Chapter 7: Similarity

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  1. Chapter7: Similarity Section 7-2: Similar Polygons

  2. Objectives • To identify similar polygons. • To apply similar polygons.

  3. Vocabulary • Similar • Similarity Ratio • Golden Rectangle • Golden Ratio

  4. Similar Figures • Similar figures are figures that have the same shape, but not necessarily the same size.

  5. Similar Polygons • Two polygons are similar if: • Corresponding angles are congruent. • Corresponding sides are proportional.

  6. Similarity Ratio • The ratio of the lengths of corresponding sides is the similarity ratio.

  7. Understanding Similarity • ABCD ~ EFGH

  8. Determining Similarity • Determine whether the triangles are similar. If they are, write a similarity statement and give the similarity ratio.

  9. Using Similar Figures • LMNO ~ QRST • Find the value of x.

  10. Golden Rectangle • A golden rectangle is a rectangle that can be divided into a square and a rectangle that is similar to the original rectangle.

  11. Golden Ratio • In any golden rectangle, the length and the width are in the golden ratio, which is about 1.618…..:1

  12. Golden Ratio in Art • The Mona Lisa is one piece of art work that contains the golden ratio.

  13. Example: Art • An artist plans to paint a picture. He wants the canvas to be a golden rectangle with its longer horizontal sides 30 cm wide. How high should the canvas be?

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