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Similarity

Concept

Similarity

Two figures are said to be similar if they can be mapped onto each other using only similarity transformations. Similarity between and is written as which reads is similar to Polygons, being defined by their angles and side lengths, are similar if two conditions are met.

  1. All corresponding angles are congruent.
  2. All pairs of corresponding sides are proportional.

For example, consider the two rectangles below:

The rectangles are similar because the ratio of the lengths is equal to the ratio of the widths. Because these ratios are equal, it can also be said that the rectangles are proportional. Some geometric figures, such as circles, spheres, squares, and cubes are always similar, or proportional, to each other.