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

Question

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 which answer is correct and why

Transitive Property of Equality
Transitive Property of Equality

Definition of congruence
Definition of congruence

Vertical Angles Theorem
Vertical Angles Theorem

Corresponding Angles Postulate
Corresponding Angles Postulate
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Answer 1

To complete the proof that consecutive interior angles are supplementary, we need to identify the proper reasoning for statement 2, which involves the relationship between angles A and E.

The most logical choice from the options presented is:

Transitive Property of Equality

Here's the reasoning:

1. From statement 1, we have \( m∠A + m∠C = 180° \) because they form a linear pair and are therefore supplementary (as stated in the reason for line 1).
2. In statement 2, we have \( m∡A = m∡E \) based on the given information (likely from a prior context where angle E is defined as congruent to angle A).
3. Thus, we can apply the Transitive Property of Equality, which states that if \( m∡A = m∡E \) and \( m∡E + m∡C = 180° \), we can conclude that \( m∡A + m∡C = 180° \).

So, the correct response is "Transitive Property of Equality" for statement 2 because it allows the substitution of angle A with angle E in the equation that states that the sum of angle E and angle C equals 180°, which follows from their relationship established in the first and second statements.