Question

In a parallelogram ABCD, E is the midpoint of AB and DE bisects angle D. Prove that: BC = BE.

Answer 1

∠CDE = ∠DEA      ...(ALternate angles)
∠CDE = ∠EDA      ...(Given DE bisects ∠D)
∠DEA = ∠EDA
⇒ AD = AE             ....(i)(Sides opposite to equal angles are equal)
Now, AD = BE        ....(ii)(Opposite to equal angles are equal)
And, AE = BE          ....(iii)(E is the mid-point of AB)
⇒ BC = BE.              ....(proved)