Question

Given: In triangle ABC, ∠B ≅ ∠C Prove: AB ≅ AC Complete the paragraph proof. We are given that ∠B ≅ ∠C. Assume segment AB is not congruent to . If AB > AC, then m∠C > m∠B by the . If AB < AC, then m∠C < m∠B by the converse of the triangle parts relationship theorem. But by the definition of congruent, we know the measure of angle B equals the measure of by the given statement. Therefore, we have a contradiction: AB = AC, and AB ≅ AC.

Answer 1

Given: In triangle ABC, ∠B ≅ ∠C

Prove: AB ≅ ACTriangle A B C is shown. Angles A B C and B C A are congruent.

Complete the paragraph proof.

We are given that ∠B ≅ ∠C. Assume segment AB is not congruent to

✔ segment AC

.

If AB > AC, then m∠C > m∠B by the

✔ converse of the triangle parts relationship theorem

. If AB < AC, then m∠C < m∠B by the converse of the triangle parts relationship theorem.

But by the definition of congruent, we know the measure of angle B equals the measure of

✔ angle C

by the given statement. Therefore, we have a contradiction: AB = AC, and AB ≅ AC.

Explanation:

Answer 2

Given: Here ABC is a triangle,

In which
`\angle B \cong \angle C`

Prove:
`AB \cong AC`

Let us assume AB is not congruent to AC.

If
`AB > AC`,

Then
`m\angle C > m\angle B` ( By the converse of the triangle parts relationship theorem )

If If AB < AC, then
`m\angle C < m\angle B` ( by the converse of the triangle parts relationship theorem. )

But, by the definition of congruent,

We know
`\angle B \cong \angle C` ( by the given statement.)

Therefore, we have a contradiction,

And,
`AB \cong AC` and
`AB = AC`.