PROOF: Given isosceles △ABC with AB¯¯¯¯¯¯¯¯≅BC¯¯¯¯¯¯¯¯ , I can construct BD←→ , the angle bisector of ∠B . Then, by the definition of an angle bisector, I know that ∠ABD≅∠CBD . I also know that line segments are congruent to themselves, so BD¯¯¯¯¯¯¯¯≅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 △ABD≅△CBD by the SAS Congruence Theorem.What statement should be placed at the end of the proof?(1 point)ResponsesFinally, corresponding parts of congruent triangles are congruent by the CPCTC Theorem, so AB¯¯¯¯¯¯¯¯≅BC¯¯¯¯¯¯¯¯. Finally, corresponding parts of congruent triangles are congruent by the CPCTC Theorem, so Modifying above upper A upper B with bar congruent to Modifying above upper B upper C with bar .Finally, ∠A≅∠C by the Base Angles Theorem.Finally, angle upper A congruent to angle upper C by the Base Angles Theorem. Finally, corresponding parts of congruent triangles are congruent by the CPCTC Theorem, so ∠A≅∠B. Finally, corresponding parts of congruent triangles are congruent by the CPCTC Theorem, so angle upper A congruent to angle upper B .Finally, corresponding parts of congruent triangles are congruent by the CPCTC Theorem, so ∠A≅∠C.

Answer 1

The correct statement to place at the end of the proof is:

"Finally, corresponding parts of congruent triangles are congruent by the CPCTC Theorem, so ∠A≅∠C by the Base Angles Theorem."

This statement correctly concludes the proof by relating the angles of the congruent triangles formed (△ABD and △CBD) to the angles ∠A and ∠C in the isosceles triangle △ABC, reinforcing the property that the base angles of an isosceles triangle are congruent.