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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

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similar polygons

Similar Polygons

Section 7.2

slide2
M.C. Escher’s Circle Limit IV
  • Winged images are the same shape but different sizes.
  • They are similar images
slide3
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
slide4
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
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
slide7
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
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
Given: The two polygons are similar.
  • Write a similarity statement: ______________
  • Write a statement of Proportionality :
  • Then find x, y and RQ:
  • Scale Factor:_____
slide10
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?
slide11
1. Find x and y.
  • 2. Scale factor: ______
  • Are they similar? why or why not?
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