Question

in the triangular prism shown below, which lines are parallel? select all that apply. bc and bd cd and fg be and eg bd and eg

Explanation:

Step1: Recall parallel - line definition

Parallel lines in 3 - D do not intersect and are in the same or parallel planes.

Step2: Analyze $\overrightarrow{BC}$ and $\overrightarrow{BD}$

They intersect at point B, so they are not parallel.

Step3: Analyze $\overrightarrow{CD}$ and $\overrightarrow{FG}$

In a triangular prism, opposite lateral - edges are parallel. $\overrightarrow{CD}$ and $\overrightarrow{FG}$ are opposite lateral - edges, so $\overrightarrow{CD}\parallel\overrightarrow{FG}$.

Step4: Analyze $\overrightarrow{BE}$ and $\overrightarrow{EG}$

They intersect at point E, so they are not parallel.

Step5: Analyze $\overrightarrow{BD}$ and $\overrightarrow{EG}$

$\overrightarrow{BD}$ and $\overrightarrow{EG}$ are in parallel planes and do not intersect, so $\overrightarrow{BD}\parallel\overrightarrow{EG}$.

Answer:

$\overrightarrow{CD}$ and $\overrightarrow{FG}$, $\overrightarrow{BD}$ and $\overrightarrow{EG}$