Similar Polygons

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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

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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
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?