Figures are mathematically similar when corresponding side lengths are related by a scale factor, and all corresponding angles are congruent. For triangles, it only matters if the corresponding angles are congruent. For rectangles, it only matters if the corresponding side lengths are related by a scale factor. All mathematically similar figures have the exact same shape. Some are bigger, and some are smaller.

Any two rectangles are similar: False.

A 3×5 rectangle is not similar to a 3×3 rectangle. Their side lengths are not related by a scale factor. You can do it by ratio too. If you set it up like a proportion, you have three over five and three over three. Three times five equals fifteen. Three times three equals nine. Fifteen and nine aren’t the same number.

Any two equilateral triangles are similar: True

All equilateral triangles have three sixty degree angles. Triangles are similar if their corresponding angles are congruent. If all angles are 60, then they’re automatically similar.