![](https://infinitestudent-migration-images.s3-us-west-2.amazonaws.com/_68f80d2f4b0f7e6b36c966004ace34eca54dbe7620160920-1233-b515vm.png)
Let us draw
DN⊥AC and BM⊥AC.
(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.