PROOF: Given isosceles triangle ABC with line AB = line BC, I can construct BD, the angle bisector of angle B. Then, by the definition of an angle bisector, I know that angles ABD = angles CBD. I also know that line segments are congruent to themselves, so line BD = line BD by the reflexive property of congruence. I now have two pairs of sides and an included angle that are congruent, so I know that triangle ABD = triangle CBD by the SAS congruence theorem. Which statement should be placed at the end of the proof?

Question

A. Finally, corresponding parts of congruent triangles are congruent by the CPTCP Theorem, so line AB = line BC
B. Finally, corresponding parts of congruent triangles are congruent by the CPTCP Theorem, so angle A = angle B
C. Finally, corresponding parts of congruent triangles are congruent by the CPTCP Theorem, so angle A = angle C.
D. Finally, angle A = angle C by the Base Angles Theorem.

Answer 1

The correct choice to conclude the proof is:

D. Finally, angle A = angle C by the Base Angles Theorem.

This is appropriate because, in an isosceles triangle (like triangle ABC, where AB = BC), the angles opposite the congruent sides (angles A and C) must also be congruent. The proof establishes the congruence of triangles ABD and CBD, thus leading to the conclusion that angles A and C are congruent by the Base Angles Theorem.