Question

In the given figure, ABCD is a ||^gm. O is any point on AC. PQ || AB and LM || AD. Prove that ar (||^gm DLOP) = ar (||^gm BMOQ)

Answer 1

Given:

(1) ABCD is a parallelogram

(2) O is any point of AC.

(3) PQ||AB and LM||AD

To prove:

Calculation:

We know that the diagonal of a parallelogram divides it into two triangles of equal area

Therefore we have

Since OC and AO are diagonals of parallelogram OQCL and AMOP respectively. Therefore

Subtracting (2) and (3) from (1) we get

Hence we get the result