Question
Huy is working on a proof that consecutive interior angles are supplementary. Statement Reason 1. m∠A+m∠C=180° Linear pairs are supplementary 2. m∠A=m∠E 3. m∠E+m∠C=180° Substitution 4. ∠E and ∠C are supplementary Definition of supplementary angles What is the missing reason in the proof? (1 point) Responses Transitive Property of Equality Transitive Property of Equality Definition of congruence Definition of congruence Corresponding Angles Postulate Corresponding Angles Postulate Vertical Angles Theorem Vertical Angles Theorem
Select One
Select One
Answers
GPT-4o mini
The missing reason in the proof you're working on is:
**Transitive Property of Equality**
This is the correct choice because, from statements 1 and 2, you establish that since \( m\angle A + m\angle C = 180^\circ \) and \( m\angle A = m\angle E \), you can substitute \( m\angle E \) for \( m\angle A \) in statement 1. Thus, leading to statement 3 which states \( m\angle E + m\angle C = 180^\circ \). This justifies the use of the Transitive Property of Equality for this proof.
**Transitive Property of Equality**
This is the correct choice because, from statements 1 and 2, you establish that since \( m\angle A + m\angle C = 180^\circ \) and \( m\angle A = m\angle E \), you can substitute \( m\angle E \) for \( m\angle A \) in statement 1. Thus, leading to statement 3 which states \( m\angle E + m\angle C = 180^\circ \). This justifies the use of the Transitive Property of Equality for this proof.