15. Di,agonals AC and BD of a quadrilateral ABCD intersect at0 in such a way that ar(AOD) = ar(BOC). Prove thatABCD is a trapezium.

Adding:: ar(AOD) + ar(AOB) =ar(AOB) + ar(B()C) i"7\ ar(ADB) = ar(ACB) ...(i) A B Triangles ADB and ACB are on the same base AB and as their areas are equal, so these must be in the same parallels. .. AB JI CD. Hence, ABCD is a trapezium.