Question

which statement is true regarding the parallel and perpendicular lines in the diagram? k || n and w ⊥ m k || n and n ⊥ m w || n and n ⊥ m w || n and w ⊥ m

Explanation:

Step1: Recall parallel - perpendicular line properties

Parallel lines lie in the same plane and never intersect. Perpendicular lines intersect at a right - angle. In the given diagram, lines \(w\) and \(n\) are in the same plane (\(H\)) and are parallel (\(w\parallel n\)). Also, line \(m\) is perpendicular to the plane \(H\), so it is perpendicular to all lines in the plane \(H\) that it intersects. Since \(w\) is in plane \(H\) and \(m\) intersects \(w\) (at the point of intersection with the plane), \(w\perp m\).

Answer:

\(w\parallel n\) and \(w\perp m\)