Figures are mathematically similar when the corresponding angles of the two figures are congruent. Two figures are also similar when they are related by a scale factor.

 

Any two rectangles are similar because even though all of the angles on a rectangle are 90 degrees. A rectangle isn’t a rectangle if all of its angles are not 90 degrees therefore proving that all rectangles are similar. There also will be a scale factor because

 

Any two equilateral triangles are similar because in order for an equilateral triangle to be an equilateral triangle all of the angles have to be 120 degrees which is 360 divided by 3. If all of the angles are congruent in an equilateral triangle, that means that any equilateral triangle is similar!