Question

in the triangular prism shown below, which lines are parallel? select all that apply.
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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 \(\overleftrightarrow{HI}\) and \(\overleftrightarrow{DE}\): In the triangular prism, \(HI\) and \(DE\) are lateral edges. Lateral edges of a prism are parallel.
• For \(\overleftrightarrow{HI}\) and \(\overleftrightarrow{DF}\): \(HI\) is a lateral edge and \(DF\) is a side of the base. They are not parallel.
• For \(\overleftrightarrow{HI}\) and \(\overleftrightarrow{EF}\): \(HI\) is a lateral edge and \(EF\) is a side of the base. They are not parallel.
• For \(\overleftrightarrow{EH}\) and \(\overleftrightarrow{FI}\): \(EH\) and \(FI\) are lateral edges. Lateral edges of a prism are parallel.

Answer:

\(\overleftrightarrow{HI}\) and \(\overleftrightarrow{DE}\), \(\overleftrightarrow{EH}\) and \(\overleftrightarrow{FI}\)