(adsbygoogle = window.adsbygoogle || []).push({}); Looking for an algebraic proof that a convex quadrilateral has intersecting diagonals

So I'm trying to find an algebraic proof that the diagonals of a convex quadrilateral intersect because I'm working on a proof of a generalization of this idea into higher dimensions and I really have no idea where to start.

Although this specifically isn't for a class, the ultimate proof that I'm working on is, so I'd rather not have anyone address the generalization.

I don't really know where to start. When discussing it in class, some people gave geometric arguments, but that's not quite what I'm looking for.

Could someone give me some pointers or at least an idea of where to start?

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Edited the title so that it wouldn't be misleading

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# An algebraic proof that a convex quadrilateral has intersecting diagonals

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