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Suppose that the parallelogram is a rhombus (a parallelogram with equal sides). If we draw the diagonals, isosceles triangles are formed (where the median is also an angle bisector and perpendicular to the base). Since the diagonals of a parallelogram bisect each other, and the diagonals don't bisect the vertex angles where they are drawn, then the parallelogram is not a rhombus.

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Q: Prove that if the diagonal of a parallelogram does not bisect the angles through the vertices to which the diagonal is drawn the parallelogram is not a rhombus?

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