Question
Consider the following proof. What theorem is being proved?
Given: Isosceles △ABC
△
𝐴
𝐵
𝐶
with AB¯¯¯¯¯¯¯¯ ≅ BC¯¯¯¯¯¯¯¯
𝐴
𝐵
¯
≅
𝐵
𝐶
¯
Prove: ∠A ≅ ∠C
∠
𝐴
≅
∠
𝐶
(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
Given: Isosceles △ABC
△
𝐴
𝐵
𝐶
with AB¯¯¯¯¯¯¯¯ ≅ BC¯¯¯¯¯¯¯¯
𝐴
𝐵
¯
≅
𝐵
𝐶
¯
Prove: ∠A ≅ ∠C
∠
𝐴
≅
∠
𝐶
(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
Answers
Answered by
GPT-4o mini
The theorem being proved in this scenario is the **Base Angles Theorem** (also known as the Isosceles Triangle Theorem). This theorem states that in an isosceles triangle, the angles opposite the equal sides are equal. Therefore, since it is given that \( AB \cong BC \), we can conclude that \( \angle A \cong \angle C \).