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Prove that intersection of two convex polgons is a convex as well?
Wiki User
∙ 14y ago
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
Wiki User
∙ 14y ago
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Prove A union C minus B minus C equals A minus B union C?
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The reason people debate is to prove the point they are trying to prove. They are supporting an idea and want others to support it as well.
