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Concept

Similar Figures

Two figures are similar figures if there is a composition of transformations that maps one figure onto the other. In other words, two figures are similar if they have the same shape and the ratios of their corresponding linear measures are equal. To denote algebraically that two figures are similar, the symbol is used.
Showing that polygons are similar.
When writing a similarity statement, the corresponding vertices must be listed in the same order. For the polygons above, two of the possible similarity statements can be written as follows.
The same definition is applicable to three-dimensional shapes.
Showing that polyhedrons are similar.
For the polyhedrons above, one of the possible similarity statements is shown below.

Among two-dimensional figures, all squares are similar and all circles are similar. Similarly, for figures, all cubes are similar and all spheres are similar.