Isosceles Triangles Answers

We are given that ΔABC is isosceles with AB ≅ AC. Using the definition of congruent line segments, we know that .

If AB > AC, then m∠C > m∠B by the . If AB < AC, then m∠C < m∠B by the converse of the triangle parts relationship theorem.

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.

However, this contradicts the given information that . Therefore, , which is what we wished to prove.