Answer:
The conclusion is ∠B and ∠C are congruent.
Step-by-step explanation:
Given a △ABC with AB ≅ AC
Since AB ≅ AC implies AB=AC.
Now as given assumption ∠B and ∠C are not congruent. Then the measure of one angle is greater than the other and if
m∠B > m∠C, then AC > AB because of the triangle parts relationship theorem.
and if m∠B < m∠C, then AC < AB by the same reason.
As we know if in a triangle two sides are equal then the triangle becomes an isosceles triangle
Since triangle is isosceles then the angles opposite to equal sides are equal i.e
if AB=AC then ∠B = ∠C in △ABC
which is contradiction to the assumption that ∠B and ∠C are not congruent.
Therefore, it can be concluded that
∠B and ∠C are congruent.
