Convex and non-convex figures

A subset $S$ of the plane is convex if, for any two points $A, B$ in $S$, the segment $AB$ is entirely contained in $S$. Otherwise, $S$ is non-convex.

Important properties

• All polygons with all interior angles less than $180^ ext{o}$ are convex.

• The intersection of convex sets is convex.

• The union of convex sets is not necessarily convex.

• Non-convex figures have at least one 'dent' or indentation.