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Similar


Of plane or solid figures, having the same shape but a different size or orientation. Two similar figures will have the same corresponding angles, and the ratio of the lengths of their corresponding sides or edges will be constant. They are, therefore, identical shapes but different sizes. Similar figures may be produced by enlargement.

For example, triangles ABC and DEF are similar triangles:

The ratio of the areas of similar plane shapes is equal to the square of the ratio of their corresponding sides. For example, a rectangle of length 8 cm and height 6 cm and a larger rectangle of length 12 cm and height 9 cm have equal ratios of length (8:12 or 1:1.5) and equal ratios of height (6:9 or 1:1.5), while the ratio of the areas of the two rectangles is 48:108, which can be reduced to 1:2.25 or 1:(1.5)2.

Similarity can apply to any two-dimensional (2D) shapes if their corresponding angles are the same.

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