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