In the adjoining figure, the diagonals AC and BD of a quadrilateral AB

1.	In the adjoining figure, the diagonals AC and BD of a quadrilateral ABCD intersect at O. If BO = OD, prove that ar (△ ABC) = ar (△ ADC).
Answer» It is given that BO = OD From the figure we know that AO is the median of △ ABD So we get Area of △ AOD = Area of △ AOB ……. (1) We know that OC is the median of △ CBD So we get Area of △ DOC = Area of △ BOC ……. (2) By adding both the equations Area of △ AOD + Area of △ DOC = Area of △ AOB + Area of △ BOC So we get Area of △ ADC = Area of △ ABC Therefore, it is proved that ar (△ ABC) = ar (△ ADC).

In the adjoining figure, the diagonals AC and BD of a quadrilateral ABCD intersect at O. If BO = OD, prove that ar (△ ABC) = ar (△ ADC).

Answer»

It is given that BO = OD

From the figure we know that AO is the median of △ ABD

So we get

Area of △ AOD = Area of △ AOB ……. (1)

We know that OC is the median of △ CBD

So we get

Area of △ DOC = Area of △ BOC ……. (2)

By adding both the equations

Area of △ AOD + Area of △ DOC = Area of △ AOB + Area of △ BOC

So we get

Area of △ ADC = Area of △ ABC

Therefore, it is proved that ar (△ ABC) = ar (△ ADC).