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

Question

Philoid · Accepted Answer

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.