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.