P and Q are any two points lying on the sides DC and AD respectively of a parallelogram ABCD. Show that area (ΔAPB) = area (ΔBQC)

ΔAPB and ||gm ABCD are on the same base AB and between the same parallel AB and DC.
Using the property, area(ΔAPB) = 1/2 area(||gm ABCD) .. (1)
Similarly, area(ΔBQC) = 1/2 area(||gm ABCD) . (2)
From (1) and (2) we have Area(ΔAPB) = Area(ΔBQC)