Answer: The required conclusion is
"if in triangle ABC, AB ≅ AC, then ∠B and ∠C must be congruent".
Step-by-step explanation: Given that in triangle ABC, AB ≅ AC, implies that AB = AC must be true. We are given to assume ∠B and ∠C are not congruent. Then the measure of one angle is greater than the other.
If m∠B > m∠C, then AC > AB because of the triangle parts relationship theorem.
For the same reason, if m∠B < m∠C, then AC < AB.
This is a contradiction to the given information.
We are to state the conclusion.
Since in the beginning, it is given that AB ≅ AC and we have assumed that ∠B and ∠C are not congruent, so
our assumption must be wrong.
That is, ∠B and ∠C must be congruent.
Thus, the required conclusion is
if in triangle ABC, AB ≅ AC, then ∠B and ∠C must be congruent.
