Question

Use the diagram to the right.
If angle∠1congruent≅angle∠​7, what theorem can you use to show that m double vertical line nm∥n​?
mm
nn
kk
jj
11
22
33
44
55
66
77
88
99
1010
1111
1212

Question content area bottom
Part 1
Choose the correct answer below.
A.
The lines are parallel by the Converse of the Corresponding Angles Theorem.
B.
The lines are parallel by the Converse of the​ Same-Side Interior Angles Theorem.
C.
The lines are parallel by the Converse of the Alternate Exterior Angles Theorem.
D.
The lines are parallel by the Converse of the Alternate Interior Angles Theorem.

Answer 1

To determine which theorem can be used, we first need to identify the relationship between the angles in the context of parallel lines and transversals.

Given that angle ∠1 is congruent to angle ∠7, we can analyze how these angles are positioned with respect to lines \( m \) and \( n \):

- If angle ∠1 and angle ∠7 are alternate exterior angles, then the lines are parallel by the Converse of the Alternate Exterior Angles Theorem.
- If angle ∠1 and angle ∠7 are corresponding angles, then the lines are parallel by the Converse of the Corresponding Angles Theorem.
- If angle ∠1 and angle ∠7 are alternate interior angles, then the lines are parallel by the Converse of the Alternate Interior Angles Theorem.
- If angle ∠1 and angle ∠7 are same-side interior angles, then the lines are parallel by the Converse of the Same-Side Interior Angles Theorem.

Since we're given that angle ∠1 is congruent to angle ∠7, we need to identify which option correctly applies to that relationship.

Assuming angle ∠1 and angle ∠7 are alternate exterior angles, the correct answer would be:

C. The lines are parallel by the Converse of the Alternate Exterior Angles Theorem.

If they were corresponding or alternate interior angles, then A or D would be correct, respectively. To select the accurate option, you'd ideally look at the specific diagram referenced, which is not provided here. However, based on the congruence of these specified angles, option C is a common answer when dealing with alternate exterior angles.