In the given figure AB = AC and BF and CE are the bisectors of angle B and C respectively. Prove that triangle EBC congruent  triangle FCB .

Since AB = AC, FB = EC.
BC = BC   (common)
ang ABC = ang ACB   (angles opposite to equal sides of a triangle are also equal)
so, ang EBC = ang FCB
​
To recap,
BC = BC
ang EBC = ang FCB
FB = EC

​So, by SAS congruence rule; Triangle EBC is congruent to Triangle FCB.

I hope this helps.  :)