Question

in the triangular prism shown below, which lines are parallel? hk and il ij and jm hj and hk jm and km

Explanation:

Step1: Recall parallel - lines in a prism

In a triangular prism, corresponding edges of the parallel bases are parallel. Also, lateral - edges are parallel.

Step2: Analyze each option

• For $\overrightarrow{HK}$ and $\overrightarrow{IL}$: $\overrightarrow{HK}$ and $\overrightarrow{IL}$ are lateral - edges of the triangular prism. Lateral - edges of a prism are parallel to each other.
• For $\overrightarrow{IJ}$ and $\overrightarrow{JM}$: $\overrightarrow{IJ}$ and $\overrightarrow{JM}$ are adjacent edges of a face, so they are not parallel.
• For $\overrightarrow{HJ}$ and $\overrightarrow{HK}$: $\overrightarrow{HJ}$ and $\overrightarrow{HK}$ are adjacent edges of a face, so they are not parallel.
• For $\overrightarrow{JM}$ and $\overrightarrow{KM}$: $\overrightarrow{JM}$ and $\overrightarrow{KM}$ are non - parallel edges of the bases.

Answer:

$\overrightarrow{HK}$ and $\overrightarrow{IL}$