Q : 3 Show that the diagonals of a parallelogram divide it into four triangles of equal area.
Let ABCD is a parallelogram. So, AB || CD and AD || BC and we know that Diagonals bisects each other. Therefore, AO = OC and BO = OD
Since OD = BO
Therefore, ar (BOC) = ar (DOC)...........(a) ( since OC is the median of triangle CBD)
Similarly, ar(AOD) = ar(DOC) ............(b) ( since OD is the median of triangle ACD)
and, ar (AOB) = ar(BOC)..............(c) ( since OB is the median of triangle ABC)
From eq (a), (b) and eq (c), we get
ar (BOC) = ar (DOC)= ar(AOD) = (AOB)
Thus, the diagonals of ||gm divide it into four equal triangles of equal area.