Question

Given: In triangle ABC, ∠B ≅ ∠C

Prove: AB ≅ ACTriangle A B C is shown. Angles A B C and B C A are congruent.

Complete the paragraph proof.

We are given that ∠B ≅ ∠C. Assume segment AB is not congruent to
.

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.

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.

Answer 1

We are given that ∠B ≅ ∠C. Assume segment AB is not congruent to AC.

If AB > AC, then m∠C > m∠B by the triangle parts relationship theorem. If AB < AC, then m∠C < m∠B by the converse of the triangle parts relationship theorem.

But by the definition of congruent, we know the measure of angle B equals the measure of angle C by the given statement. Therefore, we have a contradiction; hence AB = AC, and AB ≅ AC.