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.