The theorem being proved in the given proof is the Base Angles Theorem. This theorem states that in an isosceles triangle, the angles opposite the equal sides are congruent. In this case, the proof shows that in isosceles triangle \(ABC\) with \( AB \cong BC \), it follows that \( \angle A \cong \angle C \).
Use the image to answer the question. Consider the following proof. What theorem is being proved? Given: Isosceles △ABC with AB¯¯¯¯¯¯¯¯≅BC¯¯¯¯¯¯¯¯ Prove: ∠A≅∠C Statements Reasons1. Isosceles △ABC with AB¯¯¯¯¯¯¯¯≅BC¯¯¯¯¯¯¯¯ 1. Given2. BD←→ the angle bisector of ∠B 2. Construction3. ∠ABD≅∠CBD 3. Definition of angle bisector 4. BD¯¯¯¯¯¯¯¯≅BD¯¯¯¯¯¯¯¯ 4. Reflexive property of congruence 5. △ABD≅△CBD 5. SAS Congruence Theorem 6. ∠A≅∠C 6. CPCTC Theorem (1 point)Responsesthe Isosceles Triangle Theoremthe Isosceles Triangle Theoremthe Triangle Inequality Theorem the Triangle Inequality Theorem the Base Angles Theoremthe Base Angles Theoremthe Triangle Sum Theorem
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