In Fig, AC=AE, AB=AD and ∠BAD=∠EAC. Show that BC=DE

It is given that ∠BAD=∠EAC
∠BAD+∠DAC=∠EAC+∠DAC [add ∠DAC on both sides]
∴∠BAC=∠DAE
In ΔBAC and ΔDAE
AB=AD (Given)
∠BAC=∠DAE (Proved above)
AC=AE (Given)
∴ΔBAC≅ΔDAE (By SAS congruence rule)
∴BC=DE (By CPCT)