Question

In the figure ΔABC is isosceles with AB = AC. Prove that:
∠ADE = ∠BCD

Answer 1

In ΔADE,
∠ADE = a   ...(from (i))
In ΔBCD,
∠BCE = b  ...(AB = AC ⇒ ∠B = ∠C) .........(vii)
∠BCD = ∠BCE - ∠DCE
∠BCD = b - 2a  ...(from (vii) and (ii))
But b = 3a         ...(from (vi))
Therefore, ∠BCD = 3a - 2a = a
Hence, ∠ADE = ∠BCD.