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Question

An isosceles triangle is marked clockwise from the lower left vertex as upper A upper B upper C. The sides upper A upper B and upper B upper C are marked with single congruent tick marks.

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 Inequality Theorem
the Triangle Inequality Theorem

the Triangle Sum Theorem
the Triangle Sum Theorem

the SSS Congruence Theorem
the SSS Congruence 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 congruent sides are also congruent. In this case, since \( AB \cong BC \), it is shown that \( \angle A \cong \angle C \). The steps in the proof confirm that this is the outcome, aligning with the Base Angles Theorem.