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:

or

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