Question

ABCD is a trapezium in which its diagonals intersect at O. Show that the area of triangle AOD is equal the area of triangle BOC.

Answer 1

Assuming the parallel sides are AB and CD.

Ar(ΔACD) = Ar(ΔBDC)
(Theorem: Triangles with same base that fall between the same two parallel lines have equal areas)

=> Ar(ΔAOD)+Ar(ΔDOC) = Ar(BOC)+Ar(DOC) (sum of component triangles)
=> Ar(ΔAOD) = Ar(BOC)

Thus proved.