Question 5

Question

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

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

Transitive Property of Equality
Transitive Property of Equality

Vertical Angles Theorem
Vertical Angles Theorem

Answer 1

To complete the proof that consecutive interior angles are supplementary, we need to determine what justifies the statement that the measures of angles A and E are equal.

Given the context, we can see that angles A and E are corresponding angles formed when two parallel lines (n and m) are crossed by a transversal. According to the Corresponding Angles Postulate, when two parallel lines are intersected by a transversal, the corresponding angles are equal.

Thus, the correct response to complete the proof is:

Corresponding Angles Postulate