Which of the following statements correctly completes the proof that consecutive interior angles are supplementary?

Question

Given: n∥m
Statements Reasons
1. m∡A+m∡C=180°
1. Linear Pairs are supplementary
2. m∡A=m∡E
2. __________________________
3.. m∡E+m∡C=180°
3. Substitution
4. ∠E and ∠C
are supplementary 4. Definition of Supplementary Angles


(1 point)
Responses

Corresponding Angles Postulate
Corresponding Angles Postulate

Definition of congruence
Definition of congruence

Vertical Angles Theorem
Vertical Angles Theorem

Transitive Property of Equality

Answer 1

To complete the proof that consecutive interior angles are supplementary, the correct statement to insert for reason 2 is:

Transitive Property of Equality

This is because if m∡A = m∡E (statement 2), and we already know from step 1 that m∡A + m∡C = 180° (which implies that m∡E + m∡C = 180° through the transitive property), it logically connects the two equations.

So, the completed proof would read:

1. m∡A + m∡C = 180°
   • 1. Linear Pairs are supplementary
2. m∡A = m∡E
   • 2. Transitive Property of Equality
3. m∡E + m∡C = 180°
   • 3. Substitution
4. ∠E and ∠C are supplementary
   • 4. Definition of Supplementary Angles

Thus, the correct choice is Transitive Property of Equality.