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 Triangle Inequality Theorem the Triangle Inequality Theorem the Triangle Sum Theorem the Triangle Sum Theorem the Base Angles Theorem the Base Angles Theorem the Isosceles Triangle Theorem the Isosceles Triangle Theorem Skip to navigation

Answer 1

The theorem being proved in the given proof is the Isosceles Triangle Theorem. This theorem states that if two sides of a triangle are congruent, then the angles opposite those sides are also congruent. In this proof, it is shown that in isosceles triangle ABC, where \( AB \cong BC \), it follows that \( \angle A \cong \angle C \).