Question

ABCD is a trapezium with AB with AB || DC and diagonals AC and BD intersect at O. Prove that area of ΔAOD = area of ΔBOC.

Answer 1

Given:

• ABCD is a trapezium with AB || DC
• Diagonals AC and BD intersect at O.

To Prove: Area of ΔAOD = Area of ΔBOC.

We know that, the triangles which have same base and lie between same parallel lines have equal area

As ΔADC and ΔBDC have the same base DC and lie between same parallel lines DC and AB, we get

Area (ΔADC) = Area (ΔBDC)

⇒ Area (ΔAOD) + Area (ΔODC) = Area (ΔBOC) + Area (ΔODC)

⇒ Area (ΔAOD) = Area (ΔBOC)

Hence proved.