Question

in the rectangular prism shown below, which lines are parallel? cd and cg, bf and cg, be and de, hi and bf

Explanation:

Step1: Recall parallel - line definition

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

Step2: Analyze each option

• $\overrightarrow{CD}$ and $\overrightarrow{CG}$ intersect at point $C$, so they are not parallel.
• $\overrightarrow{BF}$ and $\overrightarrow{CG}$ are parallel. They are in parallel planes (the front - face and the right - face of the rectangular prism) and have the same direction.
• $\overrightarrow{BE}$ and $\overrightarrow{DE}$ intersect at point $E$, so they are not parallel.
• $\overrightarrow{HI}$ and $\overrightarrow{BF}$ are skew lines (not in the same plane and do not intersect), not parallel.

Answer:

$\overrightarrow{BF}$ and $\overrightarrow{CG}$