In figure, ABCD is a trapezium in which AB ∥ DC. Prove that ar(ΔAOD) = ar(ΔBOC)

Given:  ABCD is a trapezium in which AB ∥ DC

To prove: ar(ΔAOD) = ar(ΔBOC)

Proof: Since, ΔADC and ΔBDC are on the same base DC and between same parallels AB and DC

Then, ar(ΔADC) = ar(ΔBDC)

⇒ ar(ΔAOD) + ar(ΔDOC) = ar(ΔBOC) + ar(ΔDOC)

⇒ ar(ΔAOD) = ar(ΔBOC)