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Math Help - [SOLVED] Convex Polygon Proof

  1. #1
    smokeybear
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    [SOLVED] Convex Polygon Proof

    Could someone please help me with this proof?

    Prove that any polygon with interior angles at most pi is convex.

    I was trying to prove this by induction beginning with a triangle by defining planes that lie against a side of the polygon and extend to contain the polygon itself. So each point of the polygon lies inside the intersection of all such planes. I don't seem to be getting anywhere though... Any suggestions? Thanks!
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  2. #2
    MHF Contributor

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    First, my warning: I donít know the definitions, axioms, and theorems you have.
    A usual characterization of a convex polygon is: Each line determined by one of its edges is a line of support. That is, the entire polygon is a subset of the union of any line determined by one of its edges and one of its half-planes. Could that happen if an interior angle exceeds pi?
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