In the adjoining figure AC = AE, AB = AD and ∠BAD = ∠EAC, then BC is -

Given

∠BAD = ∠EAC

Concept

CPCT refers to the Corresponding parts of the Congruent Triangle.

If 2 triangles are congruent, the corresponding parts of both the triangles including the length of sides as well as angles can be inferred to be equal.

Solution

As given,

∠BAD = ∠EAC (adding ∠DAC to both sides)

∠BAD + ∠DAC = ∠EAC + ∠DAC

∠BAC = ∠DAE  

In the  △BAC and  △DAE,

AB = AD  (Given)

AC = AE  (Given)

∠BAC = ∠DAE  (Proved)

∴ △BAC ≅ △DAE (By SAS congruence rule) 

∴ BC = DE (By CPCT)

The correct option is A.