Diagonals of paralllelogram bisect each other.
therefore, PO = OR and SO = OQ
In ΔPQS, PO is median. [∵ SO = OQ]
Hence, ar (PSO) = ar(PQO) …(1)
[∵ A median of a triangle divides it into two triangles of equal areas.]
Similarly, in ΔPQR, QO is median [∵ PO = OR]
Hence, ar(PQO) = ar(QRO) …(2)
And in ΔQRS, RO is median. [∵ SO = OQ]
Hence, ar (QRO) = ar((RSO) …(3)
From the equations (1), (2) and (3), we get
ar (PSO) = ar(PQO) = ar(QRO) = ar(RSO)
Hence, in parallelogram PQRS, diagonals PR and QS Divide it into four triangles in equal area.