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 Base Angles Theorem the Base Angles Theorem the Triangle Sum Theorem the Triangle Sum Theorem the Triangle Inequality Theorem the Triangle Inequality Theorem the Isosceles Triangle Theorem

Question

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 Base Angles Theorem the Base Angles Theorem the Triangle Sum Theorem the Triangle Sum Theorem the Triangle Inequality Theorem the Triangle Inequality Theorem the Isosceles Triangle Theorem
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GPT-4o mini · Answer

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 also equal. In this case, triangle $ ABC $ is isosceles with $ AB \cong BC $, and the proof demonstrates that $ \angle A \cong \angle C $ using the properties of the isosceles triangle and congruence.