O is any point on the diagonal PR of a parallelogram PQRS (Fig.). Prove that ar (PSO) = ar (PQO).
Solution.
Given: O is any point on the diagonal PR of a parallelogram PQRS
Construction: Join QS
Let diagonals PR and QS intersect each other at T.
We know that diagonals of a parallelogram bisect each other.
\ T is the mid-point of QS and PR
Since a median of a triangle divides it into two triangle of equal area.
\ In , PT is the median of side QS
…(i)
In , OT is the median of side QS
…(ii)
Adding (i) and (ii), we have
Hence proved