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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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
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:
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?