In Fig. 15.80, ABCD is a trapezium in which AB||DC. Prove that ar(Δ AOD) = ar(Δ BOC).

Question

In Fig. 15.80, ABCD is a trapezium in which AB||DC. Prove that ar(&#x394; AOD) = ar(&#x394; BOC).

Philoid · Accepted Answer

Given that,

ABCD is a trapezium with AB ‖ DC

To prove: Area ( = Area (

Proof: Since,

ΔABC and ABD are on the same base AB and between the same parallels AB and DC

Therefore,

Area (Δ ABC) = Area (Δ ABD)

Area (Δ ABC) – Area (Δ AOB) = Area (ΔABD) – Area (Δ AOB)

Area (Δ AOD) = Area (Δ BOC)

Hence, proved