Question

which lines are parallel in the regular pentagonal prism? select each correct answer. $overleftrightarrow{cd}$ and $overleftrightarrow{he}$ $overleftrightarrow{ab}$ and $overleftrightarrow{hc}$ $overleftrightarrow{fe}$ and $overleftrightarrow{hc}$ $overleftrightarrow{he}$ and $overleftrightarrow{gf}$

Explanation:

Step1: Recall parallel - line property in prism

In a regular pentagonal prism, parallel lines are either in the same base or are lateral - edge pairs.

Step2: Analyze each option

• For $\overleftrightarrow{CD}$ and $\overleftrightarrow{HE}$: They are not parallel as they are not in the same base and not lateral - edge pairs.
• For $\overleftrightarrow{AB}$ and $\overleftrightarrow{HC}$: They are not parallel as they are not in the same base and not lateral - edge pairs.
• For $\overleftrightarrow{FE}$ and $\overleftrightarrow{HC}$: In a regular pentagonal prism, opposite sides of the pentagonal bases are parallel. $\overleftrightarrow{FE}$ and $\overleftrightarrow{HC}$ are opposite sides of the pentagonal bases, so they are parallel.
• For $\overleftrightarrow{HE}$ and $\overleftrightarrow{GF}$: They are not parallel as they are not in the same base and not lateral - edge pairs.

Answer:

$\overleftrightarrow{FE}$ and $\overleftrightarrow{HC}$