Convex and Concave Polygons

In geometry, a polygon can be either convex or concave.

Convex polygons

A convex polygon is a polygon with the following properties:

  • Every internal angle is less than 180 degrees.
  • Every line segment between two vertices of the polygon does not go exterior to the polygon (i.e., it remains inside or on the boundary of the polygon).
  • If any vertical or horizontal axis intersects it at most twice.


Concave polygons

A polygon that is not convex is called concave. A concave polygon will always have an interior angle with a measure that is greater than 180 degrees.

It is possible to cut a concave polygon into a set of convex polygons.