Question

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 that ∠B ≅ ∠C.

to prove that the sides AB = AC

This can be done by the method of contradiction.  

If possible let AB $\neq$=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.

Answer 2

Answer:

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

Step-by-step explanation: