Here is the problem:(adsbygoogle = window.adsbygoogle || []).push({});

If the diagonals of a quadrilateral intersect each other, then the quadrilateral is convex.

Proof:

Let ABCD be a convex quadrilateral. Since quadrilateral ABCD is convex, A and D are on the same side of line BC, and D and C are on the same side of line AB. Thus D is a member of the int(angle ABC). With the Crossbad theorem, BD intersect AC = {P} where C-P-R. So AC intersect BC = {Q} where D-Q-R. Since A, B, C, D are noncollinear points P=Q. So AC intersect BD = {P} = {Q}. Which proves that AC intersects PR = the empty set. Since a convex quadrilateral has the property that its diagonals intersect then ABCD is conves.

How is this? I really didn't know what to do for it. Can someone please help me with it?

Thank you!

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# Diagonals of a quadrilateral

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