In the following figure, ∠BAD = ∠EAC, BD = EC and ∠B = ∠E, then :

1. △ ABD ≇ △ AEC

2. △ ABC ≅ △ AED

3. △ ABC ≇ △ AED

4. △ ABD ≅ △ ADE

Given,

BD = EC = x (let)

∠B = ∠E

We know that,

Sides opposite to equal angles are equal.

∴ AE = AB

From figure,

BC = BD + DC = x + DC …….(1)

DE = DC + CE = DC + x …….(2)

From equations (1) and (2), we get :

BC = DE

In △ ABC and △ AED,

⇒ BC = DE (Proved above)

⇒ AB = AE (Proved above)

⇒ ∠B = ∠E (Given)

∴ △ ABC ≅ △ AED (By S.A.S. axiom)

Hence, Option 2 is the correct option.