Question

directions: decide which lines would be parallel (if any). then, choose the correct reason that justifies your decision.
(if none of the parallel lines are determined to be parallel, select
/a\ for the reason)
ex: ( k parallel n ) ( angle 3 cong angle 6 )
reason # 1

Explanation:

Step1: Analyze the angles

We are given that \(\angle1\cong\angle9\). \(\angle1\) and \(\angle9\) are alternate interior angles.

Step2: Apply the parallel - line theorem

According to the Alternate Interior Angles (AIA) Theorem, if two lines are cut by a transversal and the alternate interior angles are congruent, then the two lines are parallel. Here, lines \(k\) and \(m\) are cut by transversal \(t\), and since \(\angle1\cong\angle9\) (alternate interior angles), we can conclude that \(k\parallel m\).

Answer:

\(k\parallel m\) with the reason "If AIA \(\cong\), then lines \(\parallel\)"