Question

in the triangular prism shown below, which lines are parallel? select all that apply.
image of triangular prism with vertices d, e, f, g, h, i
options:
\overleftrightarrow{de} and \overleftrightarrow{df}
\overleftrightarrow{hi} and \overleftrightarrow{ef}
\overleftrightarrow{de} and \overleftrightarrow{fi}
\overleftrightarrow{eh} and \overleftrightarrow{fi}

Explanation:

Step1: Recall prism properties

In a triangular prism, corresponding edges of the two triangular bases are parallel, and lateral edges (connecting corresponding vertices) are parallel.

Step2: Analyze each option

• $\overline{DE}$ and $\overline{DF}$: These are edges of the top triangular base meeting at $D$, so they intersect (not parallel).
• $\overline{HI}$ and $\overline{EF}$: $\overline{HI}$ and $\overline{EF}$ are corresponding edges of the bottom and top triangular bases, so they are parallel.
• $\overline{DE}$ and $\overline{FI}$: $\overline{DE}$ and $\overline{FI}$ are lateral edges connecting corresponding vertices, so they are parallel.
• $\overline{EH}$ and $\overline{FI}$: $\overline{EH}$ and $\overline{FI}$ are lateral edges connecting corresponding vertices, so they are parallel.

Answer:

B. $\overline{HI}$ and $\overline{EF}$, C. $\overline{DE}$ and $\overline{FI}$, D. $\overline{EH}$ and $\overline{FI}$