Question

In the given figure, the diagonals AC and BD intersect at point O. If OB = OD and AB//DC, show that :

Area $\left(\Delta DOC\right)=Area\left(\Delta AOB\right)$.

If the $A\left(△DOC\right)=21$sq. units, then $A\left(△DOC\right)+A\left(△AOB\right)$ is :

Answer 1

$\angle DBA=\angle CDB$ ...[Since $AB\parallel CD$]

$\angle AOB=\angle COD$

$OB=OD$ ...Given

Hence, $\Delta DOC\cong \Delta AOB$ ....ASA test of congruence

Hence, $A\left(△AOB\right)+A\left(△DOC\right)=21+21=42$ sq. units