Question

Question:Use the image and the proof of the Base Angles Theorem to answer the question.PROOF: Given isosceles $\triangle ABC$ with $\overline{AB} \cong \overline{BC}$. I can construct $\overleftrightarrow{BD}$, the angle bisector of $\angle B$. Then, by the definition of an angle bisector, I know that $\angle ABD \cong \angle CBD$. I also know that line segments are congruent to themselves, so $\overline{BD} \cong \overline{BD}$ by the reflexive property of congruence. I now have two pairs of sides and an included angle that are congruent, so I know that $\triangle ABD \cong \triangle CBD$ by the SAS Congruence Theorem.What statement should be placed at the end of the proof?Multiple Choice Options (Responses)( ) Finally, corresponding parts of congruent triangles are congruent by the CPCTC Theorem, so $\overline{AB} \cong \overline{BC}$.( ) Finally, $\angle A \cong \angle C$ by the Base Angles Theorem.( ) Finally, corresponding parts of congruent triangles are congruent by the CPCTC Theorem, so $\angle A \cong \angle C$.( ) Finally, corresponding parts of congruent triangles are congruent by the CPCTC Theorem, so $\angle A \cong \angle B$.

Answer 1

Answer: (X) Finally, corresponding parts of congruent triangles are congruent by the CPCTC Theorem, so ∠A ≅ ∠C.

Reason: From ΔABD ≅ ΔCBD we get corresponding angles at A and C are congruent (CPCTC), which is the desired base-angles result.