Question

Use the image and the proof of the Base Angles Theorem to answer the question. 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 ∠A≅∠C.  Finally, corresponding parts of congruent triangles are congruent by the CPCTC Theorem, so  angle upper A congruent to angle upper C .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 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, corresponding parts of congruent triangles are congruent by the CPCTC Theorem, so ∠A≅∠B.

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."

This is because you have proven that triangles ΔABD and ΔCBD are congruent, and by the Corresponding Parts of Congruent Triangles are Congruent (CPCTC) theorem, the corresponding angles ∠A and ∠C must also be congruent.