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 2.________________
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

Vertical Angles Theorem
Vertical Angles Theorem

Transitive Property of Equality

Answer 1

The missing reason in the proof is the Transitive Property of Equality.

This property states that if \( a = b \) and \( b = c \), then \( a = c \). In this case, since \( m∠A = m∠E \) and from step 1 we know \( m∠A + m∠C = 180° \), we can substitute \( m∠E \) for \( m∠A \) in step 3.

So, the complete proof includes:

1. m∠A + m∠C = 180° — Linear pairs are supplementary
2. m∠A = m∠E — Transitive Property of Equality
3. m∠E + m∠C = 180° — Substitution
4. ∠E and ∠C are supplementary — Definition of supplementary angles