Question

In the adjoining figure, ABCD is a parallelogram in which AB is produced to E so that BE = AB. Prove that ED bisects BC.

Answer 1

In ∆ODC and ∆​OEB, we have:
DC = BE (∵ DC = AB)
∠COD = ∠BOE (Vertically opposite angles)
∠OCD = ∠OBE ( Alternate interior angles)

i.e., ∆​ODC ≅ ∆​OEB
⇒ OC = OB (CPCT)
We know that BC = OC + OB.
∴ ED bisects BC.