The ABC triangle is isosceles
(AB=AC)
BC=EC
you needs to be prove that ABD overlaps to AEC

ΔABD overlaps to ΔAEC
ABC triangle is isosceles => ∡B ≡ ∡C
AB = AC
∡B ≡ ∡C } => ΔABD ≡ ΔAEC => ΔABD overlaps to ΔAEC
BD = EC