Question

Daigonal AC and BD of a trapezium ABCD with AB//DC intresect each other at O. prove that Area (triangle AOD) = Area (triangle BOC).​

Answer 1

Given :-

• AC and BD are diagonals of a trapezium
• AB || DC

To prove :-

Area (∆AOD) = Area (∆BOC)

Proof :-

In the given trapezium,

∆DAB and ∆CAB lie on the same base AB and between the same parallels AB and CD.

So, their areas are equal.

→ Area of ∆DAB = Area of ∆CBA

But the required proof is to show that Area of ∆AOD is equal to Area of ∆CAB

So, we need to subtract ∆AOB on both sides to get the required proof.

Subtracting,

Area (∆DAB) - Area (∆AOB) = Area (∆CBA) - Area (∆AOB)

→ Area (∆AOD) = Area (∆BOC)

★ HENCE PROVED ★