Now in ΔABC and ΔAED
AB=AE (given )
∠ABC=∠AED (given )
And BC=ED (given)
Hence ΔABC≅ΔAED (By SAS rule)
So AC=AD ......... (1) (by CPCT)
And ∠BCA=∠EDA ......... (2) (by CPCT)
Now in ΔCAD, we know
AC=AD
So, from base angle theorem, we know
∠ACD=∠ADC .......... (3)
And ∠BCD=∠BCA+∠ACD ............ (4)
And ∠EDC=∠EDA+∠ACD
So the equation (2) and (3) we get
∠EDC=∠BCA+∠ACD ........... (5)
So from equation (4) and (5), we get
∠BCD=∠EDC