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Similar Polygons

Similar Polygons. Section 7.2. M.C. Escher’s Circle Limit IV Winged images are the same shape but different sizes. They are similar images. Similar – same shape but different size

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Similar Polygons

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  1. Similar Polygons Section 7.2

  2. M.C. Escher’s Circle Limit IV • Winged images are the same shape but different sizes. • They are similar images

  3. Similar – same shape but different size • Polygons are similar if and only if the corresponding angles are congruent and the corresponding sides are proportional. • The symbol ~ is used to show similarity

  4. Similarity statement – order is important. Corresponding sides/angles must match up just like they did in congruent triangles.

  5. Example 1 Determine whether each pair of figures is similar. Justify your answer. • All right angles are congruent, so QM. • PL and RN. • Sides opposite 90° angle • or 1.15 and or 1.15 and

  6. Is ABCD ~ EFGH?

  7. Scale factor – the ratio of corresponding sides • In example 1 the scale factor is 1.15 • In example 2 there is no scale factor

  8. Example 3 Real world • Special effects in movies are often created using miniature models. In a recent movie, a model jeep 31 inches long was created to look like a real 15-foot jeep. What is the ratio of the length of the model compared to the length of the real jeep?

  9. Given: The two polygons are similar. • Write a similarity statement: ______________ • Write a statement of Proportionality : • Then find x, y and RQ: • Scale Factor:_____

  10. Triangle JKL is similar to PQR with a scale factor of 3/4. If the sides of JKL are 6, 12, and 15 inches, what are the lengths of the sides of PQR?

  11. 1. Find x and y. • 2. Scale factor: ______ • Are they similar? why or why not?

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