Show that the diagonals of a parallelogram divide it into four triangles of equal area.

O is the mid point of AC and BD. (diagonals of bisect each other)

In \(\triangle \) ABC, BO is the median.
\(\therefore \) ar(AOB) = ar(BOC) .... (i)
also,
In \(\triangle \) BCD, CO is the median.
\(\therefore \) ar(BOC) = ar(COD) ...... (ii)
In \(\triangle \) ACD, OD is the median.
\(\therefore \) ar(AOD) = ar(COD) ....... (iii) In \(\triangle \) ABD, AO is the median.
\(\therefore \) ar(AOD) = ar(AOB) — (iv)

From equations (i), (ii), (iii) and (iv), we get,
ar(BOC) = ar(COD) = ar(AOD) = ar(AOB)

Hence, we get, the diagonals of a parallelogram divide it into four triangles of equal area.