Question

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

Explanation:

Step1: Recall the definition of parallel lines

Parallel lines are lines in a plane that do not intersect. In a triangular prism, we can use the properties of the prism's faces.

Step2: Analyze each pair

• For \(\overleftrightarrow{HI}\) and \(\overleftrightarrow{FI}\): They intersect at point \(I\), so they are not parallel.
• For \(\overleftrightarrow{GI}\) and \(\overleftrightarrow{DF}\): In the triangular prism, the lateral faces are parallelograms. The face \(GIDF\) is a parallelogram. In a parallelogram, opposite sides are parallel. So \(\overleftrightarrow{GI}\parallel\overleftrightarrow{DF}\).
• For \(\overleftrightarrow{HI}\) and \(\overleftrightarrow{DG}\): The face \(HIDG\) is a parallelogram. In a parallelogram, opposite sides are parallel. So \(\overleftrightarrow{HI}\parallel\overleftrightarrow{DG}\).
• For \(\overleftrightarrow{HI}\) and \(\overleftrightarrow{EF}\): The face \(HIEF\) is a parallelogram. In a parallelogram, opposite sides are parallel. So \(\overleftrightarrow{HI}\parallel\overleftrightarrow{EF}\).

Answer:

\(\overleftrightarrow{GI}\) and \(\overleftrightarrow{DF}\), \(\overleftrightarrow{HI}\) and \(\overleftrightarrow{DG}\), \(\overleftrightarrow{HI}\) and \(\overleftrightarrow{EF}\)