Question

∠7≅∠6
is m || n? choose your answer...
how do you know? choose your answer...

Explanation:

Step1: Recall the converse of alternate interior angles theorem

If two lines are cut by a transversal and the alternate interior angles are congruent, then the two lines are parallel.

Step2: Identify the relationship between ∠7 and ∠6

∠7 and ∠6 are alternate interior angles. Given that ∠7 ≅ ∠6.

Step3: Apply the converse of alternate interior angles theorem

Since ∠7 ≅ ∠6 (alternate interior angles are congruent), by the converse of the alternate interior angles theorem, we can conclude that \(m\parallel n\).

Answer:

Yes, \(m\parallel n\) because ∠7 and ∠6 are alternate interior angles and they are congruent. By the converse of the alternate interior angles theorem, if two lines are cut by a transversal and the alternate interior angles are congruent, then the two lines are parallel.