Question -
Answer -
O is the mid point ofAC and BD. (diagonals of bisect each other)
In ΔABC, BO is themedian.
∴ar(AOB) = ar(BOC) —(i)
also,
In ΔBCD, CO is themedian.
∴ar(BOC) = ar(COD) —(ii)
In ΔACD, OD is themedian.
∴ar(AOD) = ar(COD) —(iii)
In ΔABD, AO is themedian.
∴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, thediagonals of a parallelogram divide it into four triangles of equal area.