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

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 correctly complete the proof that consecutive interior angles are supplementary, you need a reason that justifies the equality of angles A and E.

The correct response here is:

Corresponding Angles Postulate

Here's a brief overview of how that fits into the proof:

• In statement 2, you're stating that angles A and E are equal due to their positions as corresponding angles (when two parallel lines are cut by a transversal, the corresponding angles are congruent).

So, the completed proof would look like this:

Statements Reasons

1. m∡A+m∡C=180°
2. Linear Pairs are supplementary
3. m∡A=m∡E
4. Corresponding Angles Postulate
5. m∡E+m∡C=180°
6. Substitution
7. ∠E and ∠C are supplementary
8. Definition of Supplementary Angles

Thus, the answer is Corresponding Angles Postulate.