A vertical line is intersected by two parallel lines m and n forming eight angles.
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
Vertical Angles Theorem
Vertical Angles Theorem
Transitive Property of Equality
Transitive Property of Equality
Corresponding Angles Postulate
Corresponding Angles Postulate
Definition of congruence
Definition of congruence
1 answer
The missing reason in the proof is:
Transitive Property of Equality
This is the reasoning that connects statements 1, 2, and 3. Since \( m∠A + m∠C = 180° \) (statement 1) and \( m∠A = m∠E \) (statement 2), it follows by the transitive property that \( m∠E + m∠C = 180° \) (statement 3).
