Question

in the cube shown below, which lines are parallel? select all that apply. be and dh, bf and ei, de and fg, bc and fg

Explanation:

Step1: Recall parallel - line property in cube

In a cube, parallel lines are lines that never intersect and are in the same or parallel planes.

Step2: Analyze each option

• For $\overrightarrow{BE}$ and $\overrightarrow{DH}$: They are diagonals of opposite faces of the cube. In a cube, the opposite faces are parallel, and these lines are in parallel planes and do not intersect, so they are parallel.
• For $\overrightarrow{BF}$ and $\overrightarrow{EI}$: They are edges of the cube such that they are in parallel planes and do not intersect, so they are parallel.
• For $\overrightarrow{DE}$ and $\overrightarrow{FG}$: They are non - parallel. $\overrightarrow{DE}$ is an edge on one face and $\overrightarrow{FG}$ is an edge on an adjacent non - parallel face.
• For $\overrightarrow{BC}$ and $\overrightarrow{FG}$: $\overrightarrow{BC}$ and $\overrightarrow{FG}$ are edges of the cube such that they are in parallel planes and do not intersect, so they are parallel.

Answer:

$\overrightarrow{BE}$ and $\overrightarrow{DH}$, $\overrightarrow{BF}$ and $\overrightarrow{EI}$, $\overrightarrow{BC}$ and $\overrightarrow{FG}$