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.