Let A, B and C are polygons. It is known that A is similar to A and so similarity between polygons is reflexive.
If A is similar to B then B similar to A and so similarity between polygons is symmetric.
Similarly, If A and B are both similar to C then A and B are similar as figures similar to the same rectilinear figure is also similar to one another and so similarity between polygons is transitive.
Therefore, the similarity of polygons is an equivalence relation.