Definition:Convex Polygon/Definition 5

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Definition

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 $P$.

By tangent we mean any line $l$ that contain one or more point of $P$ and has $P$ entirely in one of the half-planes created by $l$.

In this sense any line, that is spanned by a side of $P$, is tangent to $P$.

Also see

• Equivalence of Definitions of Convex Polygon

• Results about convex polygons can be found here.

Sources

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