Question

Consider the diagram and proof by contradiction.

Given: △ABC with ∠B ≅ ∠C
Prove: AB ≅ AC

Triangle A B C is shown. Angles A B C and B C A are congruent.

Which would prove that AB ≅ AC?

converse of the isosceles triangle theorem
substitution
definition of congruency
converse of the triangle parts relationship theorem

Answer 1

Converse of the isosceles triangle theorem.

Reason: In △ABC, ∠B ≅ ∠C. The converse of the isosceles triangle theorem says that if two angles of a triangle are congruent, then the sides opposite those angles are congruent. The sides opposite ∠B and ∠C are AC and AB, respectively, so AB ≅ AC.