Consider the diagram and proof by contradiction.
given: △abc with ∠b ≅ ∠c
prove: ab ≅ ac
it is given that ∠b ≅ ∠c. assume ab and ac are not congruent. if ab > ac, then m∠c > m∠b by if ac > ab, then m∠b > m∠c for the same reason. however, using the given statement and the definition of congruency, we know that m∠b = m∠c. therefore, ab = ac and ab ≅ ac.
what is the missing reason in the proof?
converse of the triangle parts relationship theorem
substitution
definition of congruency
converse of the isosceles triangle theorem

The Angle-Side Relationships theorem (or triangle parts relationship theorem) states that if one side of a triangle is longer than another side, then the angle opposite the longer side will have a greater degree measure than the angle opposite the shorter side.

The converse to the Angle-Side Relationships theorem (or triangle parts relationship theorem) states that if one angle of a triangle has a greater degree measure than another angle, then the side opposite the greater angle will be longer than the side opposite the smaller angle.

Thus, from the proof if AB > AC, then m∠C > m∠B by the converse of the triangle parts relationship theorem.