Question

1. which condition will guarantee that line l is parallel to line m? e) < 1 ≅ < 3 f) < 1 ≅ < 6 g) < 6 ≅ < 5 h) < 3 ≅ < 5

Explanation:

Step1: Recall 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.

Step2: Analyze each option

• Option E: $\angle1\cong\angle3$: These are vertical angles, not related to parallel - line criteria.
• Option F: $\angle1\cong\angle6$: These are not in a position (corresponding, alternate - interior, etc.) that would imply parallel lines.
• Option G: $\angle6\cong\angle5$: These are vertical angles, not related to parallel - line criteria.
• Option H: $\angle3\cong\angle5$: $\angle3$ and $\angle5$ are alternate interior angles. If $\angle3\cong\angle5$, then by the Alternate Interior Angles Theorem, line $l$ is parallel to line $m$.

Answer:

H. $\angle3\cong\angle5$