Question

Consider the diagram and proof by contradiction. Given: △ABC with AB ≅ AC Since it is given that AB ≅ AC, it must also be true that AB = AC. 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 what is given. Therefore, it can be concluded that ________.

Answer 1

∠B and ∠C

Explanation:

Answer 2

The conclusion is ∠B and ∠C are congruent.

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.