The theorem being proved in the given proof is the Isosceles Triangle Theorem (option c). 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 sides AB ≅ BC, it is shown that ∠A ≅ ∠C.
Consider the following proof. What theorem is being proved?
Given: Isosceles triangle ABC with AB ≅ BC
Prove: ∠A ≅ ∠C
Statements
1. Isosceles triangle ABC with AB ≅ BC
2. <--->
BD the angle bisector of ∠B
3. ∠ ABD ≅ ∠CBD
4. BD ≅ BD
5. triangle ABD ≅ triangle CBD
6. ∠A ≅ ∠C
Reasons
1. Given
2. Construction
3. Definition of angle bisector
4. Reflexive property of congruence
5. SAS Congruence Theorem
6. CPCTC Theorem
a. the Triangle Inequality Theorem
b. the Base Angles Theorem
c. the Isosceles Triangle Theorem
d. the Triangle Sum Theorem
1 answer