What do similar polygons share, aside from their similarity ratio?

Similar polygons are defined by their proportional relationships, which means that while they may differ in size, they share a fundamental property: the corresponding angles are equal. This is a defining characteristic of similar figures, as the angles allow for the determination of a consistent similarity ratio between corresponding side lengths. The equality of angles ensures that the shape remains consistent, despite potentially varying dimensions.

The idea of identical shape and size is not applicable to similar polygons, as they can vary in size but still share the same shape. The statement regarding different perimeters aligns with the nature of similar figures; even though their sides are in proportional lengths, their perimeters will differ because they are not constrained to be the same. Lastly, similar polygons do not necessarily have to have the same number of sides, as it is possible for them to belong to different families of polygons while still being similar in angle measures. Thus, the crucial property that similar polygons share is that all corresponding angles remain equal.