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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.



Assuming the parallel sides are AB and CD.

(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.
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