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, since triangle ABC is isosceles with \( AB \cong BC \), it is proven that \( \angle A \cong \angle C \).
Consider the following proof. What theorem is being proved? Given: Isosceles △ABC with AB¯¯¯¯¯¯¯¯≅BC¯¯¯¯¯¯¯¯ Prove: ∠A≅∠C Statements Reasons 1. Isosceles △ABC with AB¯¯¯¯¯¯¯¯≅BC¯¯¯¯¯¯¯¯ 1. Given 2. BD←→ the angle bisector of ∠B 2. Construction 3. ∠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) Responses the SSS Congruence Theorem the SSS Congruence Theorem the Triangle Inequality Theorem the Triangle Inequality Theorem the Triangle Sum Theorem the Triangle Sum Theorem the Base Angles Theorem
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