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 - line and perpendicular - line definitions

Parallel lines are lines that never intersect in the same plane, and perpendicular lines intersect at a 90 - degree angle.

Step2: Analyze the diagram

In the given diagram, we can see that lines \(w\) and \(n\) are in the same plane (\(\mathcal{H}\)) and are parallel (as indicated by the arrow - like symbols on them). Also, line \(m\) is perpendicular to the plane \(\mathcal{H}\), so line \(m\) is perpendicular to any line in the plane \(\mathcal{H}\) that it intersects. Since \(w\) is in the plane \(\mathcal{H}\) and intersects \(m\), \(w\perp m\).

Answer:

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