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# Similar Polygons PowerPoint PPT Presentation

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

Similar Polygons

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## 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

• 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

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

### 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

• Is ABCD ~ EFGH?

• Scale factor – the ratio of corresponding sides

• In example 1 the scale factor is 1.15

• In example 2 there is no scale factor

### 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?

### Given: The two polygons are similar.

• Write a similarity statement: ______________

• Write a statement of Proportionality :

• Then find x, y and RQ:

• Scale Factor:_____

• 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?

• 1. Find x and y.

• 2. Scale factor: ______

• Are they similar? why or why not?