Question

in the square pyramid shown below, which lines are parallel? select all that apply.

Explanation:

Step1: Recall parallel - line definition in 3 - D

Parallel lines in 3 - D do not intersect and are in the same plane or can be translated to be in the same plane. In a square pyramid, the base is a square.

Step2: Analyze base - side relationships

In square base \(PQRS\), \(\overline{PQ}\parallel\overline{RS}\) and \(\overline{QR}\parallel\overline{PS}\) because opposite sides of a square are parallel. The lateral edges (\(\overline{OQ},\overline{OP},\overline{OR},\overline{OS}\)) are not parallel to the base - sides or to each other.

Answer:

\(\overrightarrow{PQ}\) and \(\overrightarrow{RS}\)