Hey blaisem.

Do you mean that the two shapes can be rotated, scaled, and translated into each other so that they have a perfect overlap?

If this is the case then you will need to look at whether a transformation involving all of these (which can be written as matrices) exists and also if an inverse transformation exists (which it should).

Basically you have to prove that a transformation exists such that Ax = x' (transform each vertex so that you map x in shape A to x' in shape B) and that its inverse exists (determinant will be non-zero).

If you need more information look at matrix structures for translation, rotation, and scaling and compose them in the right order.