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

We know that diagonals of parallelogram bisect each other. Therefore, O is the mid-point of AC and BD

BO is the median in ΔABC. Therefore, it will divide it into two triangles of equal areas

Area (ΔAOB) = Area (ΔBOC) (i) In ΔBCD,

CO is the median

Area (ΔBOC) = Area (ΔCOD) (ii)

Similarly, Area (ΔCOD) = Area (ΔAOD) (iii)

From equations (i), (ii), and (iii), we obtain

Area (ΔAOB) = Area (ΔBOC) = Area (ΔCOD) = Area (ΔAOD)

Therefore, it is evident that the diagonals of a parallelogram divide it into four triangles of equal area