Consider the following proof. What theorem is being proved?

Question

Given: Isoscele △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 Isosceles Triangle Theorem
the Isosceles Triangle Theorem

the Base Angles Theorem
the Base Angles Theorem

the Triangle Inequality Theorem

Answer 1

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, since triangle ABC is isosceles with sides \( AB \) and \( BC \) being congruent, the proof shows that angles \( \angle A \) and \( \angle C \) are congruent as well.