Page "Similarity (geometry)" Paragraph 16

The concept of similarity extends to polygons with more than three sides.

Given any two similar polygons, corresponding sides taken in the same sequence are proportional and corresponding angles taken in the same sequence are equal in measure.

However, proportionality of corresponding sides is not by itself sufficient to prove similarity for polygons beyond triangles ( otherwise, for example, all rhombi would be similar ).

Likewise, equality of all angles in sequence is not sufficient to guarantee similarity ( otherwise all rectangles would be similar ).

A sufficient condition for similarity of polygons is that corresponding sides and diagonals are proportional.