Question

Consider the diagram and proof by contradiction.
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
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: The converse states that if two base angles of a triangle are congruent, then the sides opposite those angles are congruent. Here ∠B ≅ ∠C, so the sides opposite them (AC opposite ∠B and AB opposite ∠C) are congruent, hence AB ≅ AC.