Question

in the triangular prism shown below, which lines are parallel?
options: $overleftrightarrow{kn}$ and $overleftrightarrow{mo}$, $overleftrightarrow{jl}$ and $overleftrightarrow{kn}$, $overleftrightarrow{kn}$ and $overleftrightarrow{lo}$, $overleftrightarrow{mo}$ and $overleftrightarrow{no}$

Explanation:

Step1: Recall parallel - line property in prism

In a triangular prism, opposite edges of the rectangular faces are parallel.

Step2: Analyze each option

• $\overrightarrow{KN}$ and $\overrightarrow{MO}$: These lines are not parallel as they are not opposite edges of a rectangular face.
• $\overrightarrow{JL}$ and $\overrightarrow{KN}$: In a triangular prism, the lateral - face edges can be parallel. $\overrightarrow{JL}$ and $\overrightarrow{KN}$ are opposite edges of a rectangular lateral face, so they are parallel.
• $\overrightarrow{KN}$ and $\overrightarrow{LO}$: These lines are not parallel.
• $\overrightarrow{MO}$ and $\overrightarrow{NO}$: These lines intersect at point $O$, so they are not parallel.

Answer:

$\overrightarrow{JL}$ and $\overrightarrow{KN}$