Question

Use the image to answer the question.Huy is working on a proof that consecutive interior angles are supplementary.Statement Reason1.  m∠A+m∠C=180° Linear pairs are supplementary2.  m∠A=m∠E  3.  m∠E+m∠C=180° Substitution4.  ∠E  and  ∠C  are supplementary Definition of supplementary angles   What is the missing reason in the proof?(1 point)ResponsesVertical Angles TheoremVertical Angles TheoremCorresponding Angles PostulateCorresponding Angles PostulateTransitive Property of EqualityTransitive Property of EqualityDefinition of congruenceDefinition of congruence

Answer 1

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

Here's the reasoning:

1. Statement 1 establishes that \( m∠A + m∠C = 180° \).
2. Statement 2 states that \( m∠A = m∠E \).
3. Statement 3 uses substitution to show that \( m∠E + m∠C = 180° \), using the equality from Statement 2.
4. Finally, Statement 4 concludes that \( ∠E \) and \( ∠C \) are supplementary based on their angle measures summing to 180°.

Thus, the reason for Statement 3 where substitution is made is based on the Transitive Property of Equality, whereby if \( m∠A = m∠E \), you can substitute \( m∠E \) for \( m∠A \) in the equation for the supplementary angles.