Q17 of 109 Page 300

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.


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