Given: ∠ ABC = ∠ ACB …(i)

and ∠4 = ∠3 …(ii)

According to Euclid’s axiom, if equals are subtracted from equals, then remainders are also equal.

On subtracting Eq. (ii) from (i) ,

We get,

∠ ABC - ∠4 = ∠ ACB - ∠3

⇒ ∠1 = ∠2

Now, in ABDC, ∠1 = ∠2

⇒ DC =BD [sides opposite to equal angles are equal]