Question

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.

Answer 1

Let us draw $DN\perp ACandBM\perp AC$.
(iii) We obtained,
$Area\left(\Delta DCB\right)=Area\left(\Delta ACB\right)$
If two triangle shares the same base and equal areas, then these will lie between the same parallels.
$\Rightarrow DA||CB...\left(4\right)$
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.