Figures are mathematically similar if they share a scale factor/ratio, and also they have to have congruent corresponding angles. This is true because if there is a triangle, and both have side lengths that are related by a scale factor but don’t have angles that are congruent, the figure is not similar. In order to achieve similarity, both of these reasons have to be true.

True or False…

Any two rectangles are similar:

This is true because all rectangles’ corresponding angles are congruent. If the corresponding angles are congruent, then the shape is similar, which means that the ratio/ scale factor are the same.

Any two equilateral triangles are similar:

This is true because all equilateral triangles’ corresponding angles are congruent.  If the corresponding angles are congruent, then the shape is similar, which means that the ratio/ scale factor are the same.