Geometry
Proofs

# Prove that intersection of two convex polgons is a convex as well?

567

###### 2009-06-25 02:50:53

I will prove a more general theorem from which your answer follows immediately. Theorem: The intersection of any number (including 2) of convex polygons is convex.

Proof

Let C be the intersection of Ci which is a set of iconvex polygons. By definition of intersection, if two points A and B belong to C then they belong to every one of the Ci . But the convexity of each of the Ci tells us that line segment AB is contained in Ci . Therefore, the line segment AB is in C and because ABwas arbitrary we conclude that C is convex

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