Consider the following proof. What theorem is being proved?

Question

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 Sum Theorem
the Triangle Sum Theorem

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 Isosceles Triangle Theorem.

This theorem states that in an isosceles triangle (which has at least two equal sides), the angles opposite those equal sides are also equal. In this proof, it is established that in triangle \( \triangle ABC \), where \( AB \cong BC \), the angles \( \angle A \) and \( \angle C \) are shown to be congruent.