Figures are mathematically similar because their corresponding sides have the same ratios.

True or false:

Any two rectangles are similar.

False. Every angle on any two rectangles are 90 degrees, but the side lengths can be different. If there is a 2×3 and a 2×4 rectangle, the short side long side ratio of the 2×3 rectangle is 2/3:1, while the short side long side ratio of the 2×4 rectangle is 1/2:1.

Any two equilateral triangles are similar.

True. Every side length on an equilateral triangle must be equal, so the angles are also all 60 degrees and equal. The ratio of any equilateral triangle is always 1:1:1.