Use the image to answer the question.

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←→
is 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 Angle Sum Theorem
the Triangle Angle Sum Theorem

the Isosceles Triangle Theorem
the Isosceles Triangle Theorem

the Triangle Inequality Theorem
the Triangle Inequality Theorem

the Base Angles Theorem

Answer 1

The theorem being proved in the proof provided is the Isosceles Triangle 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 follows that \(\angle A \cong \angle C\), which is what is being demonstrated in the proof.