Take a little e from BC, make BE=BA, and connect DE.

Because BD is the bisector of ∠ABC.

So ∠ABD=EBD

And AB=EB, BD=BD.

So △ABD is equal to △EBD(SAS).

So ∠ADB=∠EDB (congruent triangles's corresponding angles are equal).

Because AB = AC. ∠ A = 108。

So ∠ ABC = ∠ ACB = 36.

So ∠ Abd = EBD = 18.

So ∠ ADB = ∠ EDB =180-(108+18) = 54.

Therefore ∠ ade = 108.

So ∠ CDE = 72

So ∠ DEC = 180-(72+36) = 72.

So ∠CDE=∠DEC

So DC = EC

So BC=BE+EC=AB+DC

So BC=AB+CD