The diagonals of quad. ABCD intersect at O .Prove that if BO = OD, then ar (triangle ABC) = ar (triangle ADC).
given: ABCD is a quadrilateral. diagonals AC and BD intersect at O. and BO=DO
TPT: area(ΔABC)=area(ΔADC)
construction: draw the perpendiculars AE and CF from A and C, such that
AE⊥BD and CF⊥BD
proof:
area(ΔBAO)=
area(ΔBAO)=area(ΔADO)...........(1)
area(ΔBOC)=
area(ΔBOC)=area(ΔDOC)............(2)
adding (1) and (2)
area(ΔBAO)+area(ΔBOC)=area(ΔADO)+area(ΔDOC)
area(ΔABC)=area(ΔADC)
which is the required result.