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Let ABCD be a convex quadrilateral. How can I prove that the area of ABC is equal to the area of ABD if and only if AB is parallel to CD?

combeenatorics
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    The triangles have a common base $AB$, hence if they have the same area, they must have the same ... ? – quasi Jan 18 '17 at 10:56

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Hint $$[ABX]=\frac{|AB|\cdot\text{dist}(AB,X)}{2}$$

Jaroslaw Matlak
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