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.

Segment AC, Converse of the triangle parts relationship theorem, Angle C in that order

Step-by-step explanation:

Given that ∠B ≅ ∠C.

to prove that the sides AB = AC

This can be done by the method of contradiction.  

If possible let AB =AC

Then either AB>AC or AB<AC

Case i:  If AB>AC, then by triangle axiom, Angle C > angle B.

But since angle C = angle B, we get AB cannot be greater than AC

Case ii:  If AB<AC, then by triangle axiom, Angle C < angle B.

But since angle C = angle B, we get AB cannot be less than AC

Conclusion:

Since AB cannot be greater than AC nor less than AC, we have only one possibility. that is AB =AC

Hence if angle B = angle C it follows that

AB = AC, and AB ≅ AC.

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step-by-step explanation:

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there are infinitely many solutions.