Question

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

Explanation:

Step1: Recall the property of parallel lines

Parallel lines are lines that never intersect and are always the same distance apart.

Step2: Analyze each pair

• For \(\overleftrightarrow{IM}\) and \(\overleftrightarrow{KL}\): In a rectangular prism, opposite edges are parallel. \(IM\) and \(KL\) are opposite vertical edges, so they are parallel.
• For \(\overleftrightarrow{JM}\) and \(\overleftrightarrow{GH}\): \(JM\) and \(GH\) are opposite vertical - like edges (in terms of orientation in the prism structure), and they are parallel.
• For \(\overleftrightarrow{FJ}\) and \(\overleftrightarrow{HL}\): \(FJ\) and \(HL\) are opposite vertical - like edges (in terms of orientation in the prism structure), and they are parallel.
• \(\overleftrightarrow{GK}\) and \(\overleftrightarrow{JK}\) intersect at point \(K\), so they are not parallel.

Answer:

\(\overleftrightarrow{IM}\) and \(\overleftrightarrow{KL}\), \(\overleftrightarrow{JM}\) and \(\overleftrightarrow{GH}\), \(\overleftrightarrow{FJ}\) and \(\overleftrightarrow{HL}\)