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## PowerPoint Slideshow about ' Similar Polygons' - avram-lang

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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 QM.
- PL and RN.
- 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?

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