Question

in the triangular prism shown below, which lines are parallel? select all that apply.

Explanation:

Step1: Recall the property of parallel lines in a triangular prism

In a triangular prism, the opposite edges of the rectangular faces are parallel.

Step2: Analyze each pair

• For \(\overrightarrow{HK}\) and \(\overrightarrow{IL}\): They are not parallel.
• For \(\overrightarrow{GI}\) and \(\overrightarrow{JK}\): Since \(GI\) and \(JK\) are opposite edges of a rectangular face, they are parallel.
• For \(\overrightarrow{GJ}\) and \(\overrightarrow{KL}\): Since \(GJ\) and \(KL\) are opposite edges of a rectangular face, they are parallel.
• For \(\overrightarrow{GI}\) and \(\overrightarrow{HJ}\): Since \(GI\) and \(HJ\) are opposite edges of a rectangular face, they are parallel.

Answer:

\(\overrightarrow{GI}\) and \(\overrightarrow{JK}\), \(\overrightarrow{GJ}\) and \(\overrightarrow{KL}\), \(\overrightarrow{GI}\) and \(\overrightarrow{HJ}\)