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 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
Answers
GPT-4o mini
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
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