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.

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parmesanchilliwack parmesanchilliwack · Answer 1 · 2019-01-18T06:57:26+01:00

Answer:

Given: Here ABC is a triangle,

In which [tex]\angle B \cong \angle C[/tex]

Prove: [tex]AB \cong AC[/tex]

Let us assume AB is not congruent to AC.

If [tex]AB > AC[/tex],

Then [tex]m\angle C > m\angle B[/tex] ( By the converse of the triangle parts relationship theorem )

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

But, by the definition of congruent,

We know [tex]\angle B \cong \angle C[/tex] ( by the given statement.)

Therefore, we have a contradiction,

And, [tex]AB \cong AC[/tex] and [tex]AB = AC[/tex].

kilylittle8 kilylittle8 · Answer 2 · 2022-03-12T05:15:29+01:00

Answer:

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.

Step-by-step explanation: