Triangle Inequalities Answers

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 .

But by the definition of congruent, we know the measure of angle B equals the measure of by the given statement. Therefore, we have a contradiction: AB = AC, and AB ≅ AC.