In ΔABC, m∠B = m∠C. The angle bisector of ∠B meets AC at point H and the angle bisector of ∠C meets
AB at point K. Prove that BH≅CK

First, let's illustrate the problem as shown in the picture attached. Then, let's make a two-column proof:

           Statement                                                       Reason

         m∠B = m∠C                                                       Given

            AB = AC                                        Isosceles Triangle Definition

      AK=KB=AH=HC                                      Angle Bisector Postulate

       ΔBKC = ΔHBC                                        Line BC is common side

            BH = CK   Corresponding parts of congruent triangles are congruent

by definition, an arc subtended by a central angle of some given measure has the same measure. so .