Question

in the triangular prism shown below, which lines are parallel?
options: (overleftrightarrow{gi}) and (overleftrightarrow{hi}), (overleftrightarrow{de}) and (overleftrightarrow{gh}), (overleftrightarrow{hi}) and (overleftrightarrow{fi}), (overleftrightarrow{dg}) and (overleftrightarrow{gh})

Explanation:

Step1: Recall parallel - line property

Parallel lines in 3 - D shapes do not intersect and are in the same or parallel planes. In a triangular prism, the corresponding edges of the two parallel triangular bases are parallel.

Step2: Analyze each option

• $\overleftrightarrow{GI}$ and $\overleftrightarrow{HI}$ intersect at point $I$, so they are not parallel.
• $\overleftrightarrow{DE}$ and $\overleftrightarrow{GH}$ are corresponding edges of the two parallel triangular bases ($\triangle DEF$ and $\triangle GHI$), so they are parallel.
• $\overleftrightarrow{HI}$ and $\overleftrightarrow{FI}$ intersect at point $I$, so they are not parallel.
• $\overleftrightarrow{DG}$ and $\overleftrightarrow{GH}$ intersect at point $G$, so they are not parallel.

Answer:

$\overleftrightarrow{DE}$ and $\overleftrightarrow{GH}$