Q : 3 P and Q are any two points lying on the sides DC and AD respectively of a parallelogram ABCD. Show that .
ABCD is a parallelogram, therefore AB || CD and BC || AD.
Now, APB and ||gm ABCD are on the same base AB and between two parallels AB and DC.
Therefore, ar (APB) = 1/2 . ar(||gm ABCD)...........(i)
Also, BQC and ||gm ABCD are on the same base BC and between two parallels BC and AD.
Therefore, ar(BQC) = 1/2 . ar(||gmABCD)...........(ii)
From eq(i) and eq (ii), we get,
ar (APB) = ar(BQC)