Similarly, if m∠B is less than m∠C, we would reach the contradiction that AB > AC. Therefore, the angles must be congruent.
We are given that ΔABC is isosceles with AB ≅ AC. Using the definition of congruent line segments, we know that .:AB = AC
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 .:angle A is congruent to angle C
However, this contradicts the given information that . Therefore, , which is what we wished to prove.:side AB is congruent to side AC
However, this contradicts the given information that . Therefore, , which is what we wished to prove.:angle B is congruent to angle C