We are given that ∠B ≅ ∠C. Assume segment AB is not congruent to .:
segment AC
If AB > AC, then m∠C > m∠B by the . If AB < AC, then m∠C < m∠B by the converse of the triangle parts relationship theorem.:
converse of the triangle parts relationship theorem
But by the definition of congruent, we know the measure of angle B equals the measure of by the given statement. Therefore, we have a contradiction: AB = AC, and AB ≅ AC.: