Consider the diagram and proof by contradiction. Given: △ABC with AB ≅ AC

Triangle A B C is shown. The lengths of sides A B and A C are congruent.

Since it is given that AB ≅ AC, it must also be true that AB = AC. Assume ∠B and ∠C are not congruent. Then the measure of one angle is greater than the other. If m∠B > m∠C, then AC > AB because of the triangle parts relationship theorem. For the same reason, if m∠B < m∠C, then AC < AB. This is a contradiction to what is given. Therefore, it can be concluded that .

AB ≠ AC
∠B ≅ ∠C
ABC is not a triangle
∠A ≅ ∠B ≅ ∠C