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 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 Transitive Property of Equality Transitive Property of Equality Definition of congruence Definition of congruence Corresponding Angles Postulate Corresponding Angles Postulate Vertical Angles Theorem

Answer 1

To find the missing reason in Huy's proof, we need to look closely at the statements provided.

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)

The missing reason needs to justify why m∠E + m∠C = 180° based on the previous steps. Given that m∠A = m∠E, we substitute m∠E for m∠A in the first statement.

Thus, the reason for step 3 should be the Transitive Property of Equality since it is stating that if m∠A = m∠E and we already know m∠A + m∠C = 180°, we can replace m∠A with m∠E.

Correct answer:

Transitive Property of Equality