Given: ΔABC is isosceles; AB ≅ AC Prove: ∠B ≅ ∠C Triangle A B C is shown. Sides B A and A C are congruent. We are given that ΔABC is isosceles with AB ≅ AC. Using the definition of congruent line segments, we know that . Let’s assume that angles B and C are not congruent. Then one angle measure must be greater than the other. If m∠B is greater than m∠C, then AC is greater than AB by the . However, this contradicts the given information that . Therefore, , which is what we wished to prove. Similarly, if m∠B is less than m∠C, we would reach the contradiction that AB > AC. Therefore, the angles must be congruent.