Consider the diagram and proof by contradiction.

Given: △ABC with ∠B ≅ ∠C
Prove: AB ≅ AC

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.

What is the missing reason in the proof?

converse of the triangle parts relationship theorem
substitution
definition of congruency
converse of the isosceles triangle theorem

The Angle-Side Relationships theorem (or triangle parts relationship theorem) states that if one side of a triangle is longer than another side, then the angle opposite the longer side will have a greater degree measure than the angle opposite the shorter side.

The converse to the Angle-Side Relationships theorem (or triangle parts relationship theorem) states that if one angle of a triangle has a greater degree measure than another angle, then the side opposite the greater angle will be longer than the side opposite the smaller angle.

Thus, from the proof if AB > AC, then m∠C > m∠B by the converse of the triangle parts relationship theorem.

jainveenamrata jainveenamrata · Answer 2 · 2022-02-08T10:04:21+01:00

The correct statement is that it is done by the converse of the triangle parts relationship theorem.

What is the triangle?

Triangle is a polygon that has three sides and three angles. The sum of the angle of the triangle is 180 degrees.

Isosceles triangle

Two sides of the triangle are equal and their opposite angles too.

Given

△ABC with ∠B ≅ ∠C

Prove that

AB ≅ AC

How to give a conclusion?

From the definition of the Isosceles triangle, it is proved that if ∠B ≅ ∠C Then AB ≅ AC.

We know that if the length o the side increases then the opposite angle decreases.

It is done by the converse of the triangle parts relationship theorem.

More about the triangle link is given below.

https://brainly.com/question/25813512