Question

It is given that ∠B ≅ ∠C. Assume AB and AC are not congruent. If AB > AC, then m∠C > m∠B by ________. If AC > AB, then m∠B > m∠C for the same reason. However, using the given statement and the definition of congruency, we know that m∠B = m∠C. Therefore, AB = AC and AB ≅ AC.

Answer 1

Its converse of the triangle parts relationship theorem

Answer 2

It is given that ∠B ≅ ∠C. Assume AB and AC are not congruent. If AB > AC, then m∠C > m∠B by the triangle parts relationship theorem. If AC > AB, then m∠B > m∠C for the same reason.

However, using the given statement and the definition of congruency, we know that m∠B = m∠C.

Therefore, AB = AC and AB ≅ AC.