Suppose ABC is an

BD and CE are bisectors of ∠B and ∠C

∠ABD = ∠DBC

∠ACE = ∠BCE

Since Δ ABC is isosceles so

∠ABC = ∠ACB …(i)

Since BD and CE are bisectors so

2∠DBC = 2∠ECB

⇒ ∠DBC = ∠ECB …(ii)

BC = BC (Common) …(iii)

From (i) , (ii) and (iii) we can say

Δ BCE and Δ BCD are congruent to each other by A.A.S. axiom of congruency

So we can say

BD = EC (Corresponding parts of Congruent triangles)