In the adjoining figure, ABCD is a parallelogram whose diagonals intersect each other at O.

Question:

In the adjoining figure, ABCD is a parallelogram whose diagonals intersect each other at OA line segment EOF is drawn to meet AB at E and DC at F. Prove that OE = OF.

 

Solution:

In ∆​ODF and ∆​OBE, we have:
OD = OB                                  (Diagonals bisects each other)
DOF = ∠BOE                         (Vertically opposite angles)
∠FDO = ∠OBE                         (Alternate interior angles)
 i.e., ∆​ODF ≅ ∆​OBE
∴​ OF = OE                                 (CPCT)
Hence, proved.

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