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