Question

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

Explanation:

Step1: Recall parallel - line definition

Parallel lines in 3 - D (in the context of the pyramid) are lines that lie in the same plane and do not intersect.

Step2: Analyze base of the square - pyramid

The base of the square - pyramid is a square. In a square, opposite sides are parallel. Here, in the base square \(LMNO\), \(\overrightarrow{LO}\) and \(\overrightarrow{MN}\) are opposite sides of the square base.

Step3: Analyze other pairs

• \(\overrightarrow{MN}\) and \(\overrightarrow{OP}\): \(\overrightarrow{OP}\) is an edge connecting the apex to a vertex of the base and \(\overrightarrow{MN}\) is a base - edge, they are not parallel.
• \(\overrightarrow{LM}\) and \(\overrightarrow{NO}\): \(\overrightarrow{LM}\) and \(\overrightarrow{NO}\) are adjacent sides of the base square, so they are not parallel.
• \(\overrightarrow{NO}\) and \(\overrightarrow{NP}\): \(\overrightarrow{NP}\) is an edge connecting the apex to a vertex of the base and \(\overrightarrow{NO}\) is a base - edge, they are not parallel.

Answer:

\(\overrightarrow{LO}\) and \(\overrightarrow{MN}\)