Question

in the rectangular prism shown below, which lines are intersecting? select all that apply. $overleftrightarrow{hk}$ and $overleftrightarrow{dh}$, $overleftrightarrow{jk}$ and $overleftrightarrow{ei}$, $overleftrightarrow{dg}$ and $overleftrightarrow{ei}$, $overleftrightarrow{hi}$ and $overleftrightarrow{ef}$

Explanation:

Step1: Recall intersecting lines definition

Intersecting lines meet at a point.

Step2: Analyze $\overrightarrow{HK}$ and $\overrightarrow{DH}$

They meet at point $H$, so they are intersecting.

Step3: Analyze $\overrightarrow{JK}$ and $\overrightarrow{EI}$

They are skew - not in the same plane and do not intersect.

Step4: Analyze $\overrightarrow{DG}$ and $\overrightarrow{EI}$

They are skew - not in the same plane and do not intersect.

Step5: Analyze $\overrightarrow{HI}$ and $\overrightarrow{EF}$

They are parallel and do not intersect.

Answer:

$\overrightarrow{HK}$ and $\overrightarrow{DH}$