Similar Polygons

Consider the polygons ABCD and A'B'C'D 'in the figures:

Notice that:

  • the corresponding angles are congruent:

  • the corresponding (or homologous) sides are proportional:


We can conclude that the polygons ABCD and A'B'C'D 'are similar and we indicate:

ABCD ~ A'B'D'C '(reads "polygon ABCD is similar to polygon A'B'D'C'")

That is:

Two polygons are similar when the corresponding angles are congruent and the corresponding sides are proportional.

The ratio between two corresponding sides in similar polygons is called similarity ratio, that is:

The similarity ratio of the polygons considered is

Note: The definition of similar polygons is only valid when both conditions are satisfied:

  • congruent matching angles
  • proportional matching sides

Just one of the conditions is not sufficient to indicate the similarity between polygons.

Next: Polygon Similarity Properties