Question

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

Explanation:

Step1: Recall the properties of a triangular prism

In a triangular prism, the corresponding sides of the two triangular bases are parallel, and the lateral edges are parallel.

Step2: Analyze each pair

• For \(\overleftrightarrow{MN}\) and \(\overleftrightarrow{MO}\): These are two sides of the same triangular face \( \triangle MNO\), they are not parallel.
• For \(\overleftrightarrow{KL}\) and \(\overleftrightarrow{NO}\): In a triangular prism, the corresponding sides of the two triangular bases (\(\triangle KLJ\) and \(\triangle MNO\)) are parallel. So \(\overleftrightarrow{KL}\parallel\overleftrightarrow{NO}\).
• For \(\overleftrightarrow{JK}\) and \(\overleftrightarrow{MO}\): In a triangular prism, the lateral edges are parallel. So \(\overleftrightarrow{JK}\parallel\overleftrightarrow{MO}\).
• For \(\overleftrightarrow{JL}\) and \(\overleftrightarrow{LO}\): These are two sides of the quadrilateral face \(JLON\), they are not parallel.

Answer:

\(\overleftrightarrow{KL}\) and \(\overleftrightarrow{NO}\), \(\overleftrightarrow{JK}\) and \(\overleftrightarrow{MO}\)