Figures are mathematically similar when all corresponding angles are congruent. Always have to check if the corresponding sides are related by a scale factor. Also the shapes have to have the same general shape. 

True or false

Any too rectangles are similar: False

Because all shapes that are similar have to follow all the rules that are listed above.

Any two equilateral triangles are similar: true

Because all equilateral triangles have corresponding sides and angles that are congruent. Also an equilateral triangle definitely has the same general shape as another equilateral triangle.