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.