In the given figure, AD ⊥ BC and AB = AC, then :

1. △ ABD ≇ △ ACD

2. BD = CD

3. ∠BAC = 90°

4. ∠CAD = 45°

We know that,

Angles opposite to equal sides are equal.

Since, AB = AC,

∴ ∠C = ∠B.

In △ ABD and △ ACD,

⇒ AB = AC (Given)

⇒ AD = AD (Common side)

⇒ ∠B = ∠C (Proved above)

∴ △ ABD ≅ △ ACD (By S.A.S. axiom)

We know that,

Corresponding sides of congruent triangles are equal.

∴ BD = CD.

Hence, Option 2 is the correct option.