Complete the paragraph proof. We are given that ∠B ≅ ∠C. Assume segment AB is not congruent to . If AB > AC, then m∠C > m∠

Question

27 days ago

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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.

Mathematics

2 answers:

lawyer [9.2K] · Answer 1 · 2026-03-01T03:02:51+03:00

lawyer [9.2K]27 days ago

6 0

Conclusion:

Segment AC, converse of the triangle parts relationship theorem, and Angle C in that sequence

Detailed explanation:

Inessa [9K] · Answer 2 · 2026-03-01T03:03:14+03:00

Using the information that ∠B ≅ ∠C,

we need to demonstrate that sides AB and AC are equal.

This can be shown using a proof by contradiction.

Assume for the sake of argument that AB $\neq$ is not equal to AC.

This means either AB > AC or AB < AC.

Case i: If AB > AC, then according to the triangle axiom, Angle C must be greater than angle B.

However, given that Angle C = Angle B, we see that AB cannot be greater than AC.

Case ii: If AB < AC, then by the triangle axiom, Angle C would have to be less than angle B.

Since Angle C = Angle B, we conclude that AB cannot be less than AC either.

Conclusion:

Therefore, since AB cannot be either greater than or less than AC, we are left with only one possibility, which is that AB = AC.

Thus, from the fact that angle B equals angle C, we deduce that

AB = AC, and AB ≅ AC.