Question

in the rectangular prism shown below, which lines are parallel? select all that apply.

Explanation:

Step1: Recall parallel - line property in prism

In a rectangular prism, opposite edges are parallel.

Step2: Analyze $\overleftrightarrow{HK}$ and $\overleftrightarrow{IJ}$

$HK$ and $IJ$ are opposite vertical edges, so $\overleftrightarrow{HK}\parallel\overleftrightarrow{IJ}$.

Step3: Analyze $\overleftrightarrow{HL}$ and $\overleftrightarrow{IM}$

$HL$ and $IM$ are opposite horizontal - parallel edges on different faces, so $\overleftrightarrow{HL}\parallel\overleftrightarrow{IM}$.

Step4: Analyze $\overleftrightarrow{IJ}$ and $\overleftrightarrow{LO}$

$IJ$ and $LO$ are opposite horizontal - parallel edges on different faces, so $\overleftrightarrow{IJ}\parallel\overleftrightarrow{LO}$.

Step5: Analyze $\overleftrightarrow{HK}$ and $\overleftrightarrow{LO}$

Since $\overleftrightarrow{HK}\parallel\overleftrightarrow{IJ}$ and $\overleftrightarrow{IJ}\parallel\overleftrightarrow{LO}$, by the transitive property of parallel lines, $\overleftrightarrow{HK}\parallel\overleftrightarrow{LO}$.

Answer:

$\overleftrightarrow{HK}$ and $\overleftrightarrow{IJ}$, $\overleftrightarrow{HL}$ and $\overleftrightarrow{IM}$, $\overleftrightarrow{IJ}$ and $\overleftrightarrow{LO}$, $\overleftrightarrow{HK}$ and $\overleftrightarrow{LO}$