In the adjoining figures, is a parallelogram whose diagonals intersect each other at A line segment is drawn to meet at and at Prove that

ABCD is parallelogram.

∴ in ∆​ODF and ∆​OBE, we have:

OD = OB … Diagonals bisects each other
∠DOF = ∠BOE … Vertically opposite angles
∠FDO = ∠OBE … Alternate interior angles

Hence, by SAA test for congruency,
∆​ODF ≅ ∆​OBE
∴​ OF = OE …by cpct
Hence, proved.