Solution
Given
AB = AC and AD = AB
To Prove
BCD is a right angle
Proof
In ∆ABC,
AB=AC
∠ACB=∠ABC ——————–(i)
In ∆ACD,
AC=AD
∠ACD=∠ADC ——————–(ii)
On adding equations (i) and (ii) we get
∠ACB+∠ACD=∠ABC+∠ADC
∠BCD=∠ABC+∠BDC
Adding ∠BCD on both side
∠BCD+∠BCD=∠ABC+∠BDC+∠BCD
2∠BCD=180°
∠BCD=(180°)/2=90°
Hence Proved