Question

in the triangular prism shown below, which lines are parallel? $overrightarrow{il}$ and $overrightarrow{kl}$ $overrightarrow{jm}$ and $overrightarrow{lm}$ $overrightarrow{ij}$ and $overrightarrow{lm}$ $overrightarrow{hi}$ and $overrightarrow{ij}$

Explanation:

Step1: Recall parallel - line property in prism

In a triangular prism, parallel lines are those that lie in parallel planes and do not intersect.

Step2: Analyze each option

• $\overrightarrow{IL}$ and $\overrightarrow{KL}$ intersect at point $L$, so they are not parallel.
• $\overrightarrow{JM}$ and $\overrightarrow{LM}$ intersect at point $M$, so they are not parallel.
• $\overrightarrow{IJ}$ and $\overrightarrow{LM}$ are in parallel planes of the triangular - prism and do not intersect, so they are parallel.
• $\overrightarrow{HI}$ and $\overrightarrow{IJ}$ intersect at point $I$, so they are not parallel.

Answer:

$\overrightarrow{IJ}$ and $\overrightarrow{LM}$