Q: 4 In Fig. , P is a point in the interior of a parallelogram ABCD. Show that
[Hint : Through P, draw a line parallel to AB.]
We have a ||gm ABCD and AB || CD, AD || BC. Through P, draw a line parallel to AB
Now, APB and ||gm ABEFare on the same base AB and between the same parallels EF and AB.
Therefore, ar (APB) = 1/2 . ar(ABEF)...............(i)
Similarly, ar (PCD ) = 1/2 . ar (EFDC) ..............(ii)
Now, by adding both equations, we get