Question

in the cube shown below, which lines are parallel? select all that apply.
ad and cd
bc and bf
ae and cg
bc and ef

Explanation:

Step1: Recall parallel - lines definition

In a 3 - D space (like a cube), parallel lines are lines that do not intersect and are in the same plane.

Step2: Analyze each pair

• $\overrightarrow{AD}$ and $\overrightarrow{CD}$ intersect at point $D$, so they are not parallel.
• $\overrightarrow{BC}$ and $\overrightarrow{BF}$ intersect at point $B$, so they are not parallel.
• $\overrightarrow{AE}$ and $\overrightarrow{CG}$: In a cube, $AE\parallel CG$. They are in parallel planes (e.g., planes $ABFE$ and $DCGH$) and do not intersect.
• $\overrightarrow{BC}$ and $\overrightarrow{EF}$: In a cube, $BC\parallel EF$. They are in parallel planes (e.g., planes $ABCD$ and $EFGH$) and do not intersect.

Answer:

$\overrightarrow{AE}$ and $\overrightarrow{CG}$, $\overrightarrow{BC}$ and $\overrightarrow{EF}$