Question

refer to the figure. which statement is true? a. (l_1perp t) and (l_2parallel l_3) b. (l_1perp t) and (l_2
parallel l_3) c. (l_1parallel l_2parallel l_3) d. (l_1
parallel l_2) and (l_3perp t) e. (l_1
parallel l_2
parallel l_3)

Explanation:

Step1: Check perpendicular - parallel relationships

Since the angle between \(l_1\) and \(t\) is \(90^{\circ}\), by the definition of perpendicular lines (two lines are perpendicular if the angle between them is \(90^{\circ}\)), \(l_1\perp t\).

Step2: Analyze \(l_2\) and \(l_3\)

The corresponding angles formed by the transversal and \(l_2\), \(l_3\) are equal (\(60^{\circ}\)). By the converse of corresponding - angles postulate (if two lines are cut by a transversal and the corresponding angles are equal, then the two lines are parallel), \(l_2\parallel l_3\).

Answer:

A. \(l_1\perp t\) and \(l_2\parallel l_3\)