Definition:Convex Polygon

This page is about convex polygon. For other uses, see convex.

Definition

Definition 1

Let $P$ be a polygon.

$P$ is a convex polygon if and only if:

For all points $A$ and $B$ located inside $P$, the line $AB$ is also inside $P$.

Definition 2

Let $P$ be a polygon.

$P$ is a convex polygon if and only if:

every internal angle of $P$ is not greater than $180 \degrees$.

Definition 3

Let $P$ be a polygon.

$P$ is a convex polygon if and only if:

the region enclosed by $P$ lies entirely on the same side of each side of $P$

Definition 4

Let $P$ be a polygon.

$P$ is a convex polygon if and only if:

the region enclosed by $P$ is the intersection of a finite number of half-planes.

Definition 5

Let $P$ be a polygon.

$P$ is a convex polygon if and only if:

the region enclosed by $P$ is the intersection of all half-planes that contain $P$ and that are created by all the lines that are tangent to $P$.

Also see

• Equivalence of Definitions of Convex Polygon

• Definition:Concave Polygon

• Results about convex polygons can be found here.