Figures are mathematically similar when..

When all of the corresponding angles are congruent.

When there is a scale factor between the two shapes.

True or False

Any two rectangles are similar :

1) All the angles are the same (90 degrees).
2) If you have two rectangles, the sides of one could be 1 and 2 units. For the other they could be 1 and 3 units. The sides do not have the same proportions. One is 1:1 and the the other is 2:3.
So rectangles are not all similar.

Any two equilateral triangles are similar :

For the equilateral triangles since they always have 3 angles that are each 60°, any 2 equilateral triangles will be similar.