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Question 6 (iii)
In the given figure, diagonals AC and BD of quadrilateral ABCD intersect at O such that OB = OD. If AB = CD, then show that:
(iii) DA || CB or ABCD is a parallelogram.

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Solution


Let us draw DNAC and BMAC.
(iii) We obtained,
Area(ΔDCB)=Area(ΔACB)
If two triangle shares the same base and equal areas, then these will lie between the same parallels.
DA||CB...(4)
In quadrilateral ABCD, one pair of opposite sides are equal (AB = CD) and the other pair of opposite sides is parallel (DA || CB).
Therefore, ABCD is a parallelogram.

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