Huy is working on a proof that consecutive interior angles are supplementary.

Question

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

Corresponding Angles Postulate
Corresponding Angles Postulate

Definition of congruence
Definition of congruence

Vertical Angles Theorem
Vertical Angles Theorem

Transitive Property of Equality

Answer 1

The missing reason in the proof is:

Transitive Property of Equality

The proof uses this property when it states that if \( m\angle A = m\angle E \) and \( m\angle E + m\angle C = 180° \), then it can conclude that \( m\angle A + m\angle C = 180° \) by substituting \( m\angle E \) for \( m\angle A \). This is an application of the Transitive Property.