Which of the following is true for the given figure :

1. △ ABD ≅ △ ACD

2. angle BAD ≠ angle CAD

3. △ ABD ≇ △ ACD

4. ∠EAB = ∠BAD

From figure,

⇒ ∠EAD = ∠FAD = 90°

⇒ ∠EAB = ∠FAC = x (let)

⇒ ∠BAD = ∠EAD - ∠EAB = 90° - x

⇒ ∠CAD = ∠FAD - ∠FAC = 90° - x.

∴ ∠BAD = ∠CAD.

In △ ABD and △ ACD,

⇒ AD = AD (Common side)

⇒ ∠ADB = ∠ADC (Both equal to 90°)

⇒ ∠BAD = ∠CAD (Proved above)

∴ △ ABD ≅ △ ACD (By A.S.A. axiom)

Hence, Option 1 is the correct option.