Figures are mathematically similar when their side lengths are in a true proportion. You can use a ratio to find out if two shapes are similar. You find the ratio for the two shapes and cross multiply. If the two answers are the same, they are similar. Another way to find if two shapes are similar is by scale factor. A scale factor is a number that you can use to multiply the sides of a figure to get the corresponding side of a similar figure. Another way to tell if two shapes are similar is if they have similar shapes and the corresponding angles are congruent.

Any two rectangles are similar. FALSE. Two rectangles aren’t always similar because they don’t always have a scale factor. One rectangle could be 3 by 8 and another could be 5 by 9. There is no scale factor between these two shapes. All rectangles have similar shapes and corresponding angles that are similar, but that doesn’t mean that they have a scale factor or a true proportion.

Any two equilateral triangles are similar. TRUE. All equilateral triangles have the same general shape and the same angles, so even if the sizes and dimensions are different, they still have the same shapes and they are still similar.