Figures are mathematically similar if…

All corresponding(the ones that match up with the other figure) angles are congruent(the same).

Figures must have the same general shape.

Areas and perimeters must be related by a scale factor.

Side lengths are related by a ratio.

True or False…

1. Any two rectangles are similar.
2. Any two equilateral triangles are similar.

1. False because although they have the same general shape and the corresponding angles are congruent, Depending on the rectangle there might not be a scale factor or ratio relating the two rectangles. Some rectangles will be similar, but not all.
2. True because all corresponding angles are congruent. The definition of a equilateral triangle is that all their angles are the same. Which makes all the side lengths equal to each other. And that means that a ratio and scale factor are made as soon as create those two equilateral triangles.