Given : A parallelogram ABCD in which AC is the diagonal and O is some point on the diagonal AC

To prove: area(∆AOB) = area(∆AOD)

Construction : Draw a diagonal BD and mark the intersection as P

Proof:

We know that in a parallelogram diagonals bisect each other, hence P is the midpoint of ∆ABD

Area of (∆APB) = Area of (∆APD)—1

Now consider ∆BOD here OP is the median, since P is the midpoint of BD

Area of (∆OPB) = Area of (∆OPD)—2

Adding –1 and –2 we get

Area of (∆APB) + Area of (∆OPB) = Area of (∆APD) + Area of (∆OPD)

Area of (∆AOB) = Area of (∆AOD)

Hence proved