Question

which lines are parallel in the triangular prism? select each correct answer. □ $overleftrightarrow{ad}$ and $overleftrightarrow{bc}$ □ $overleftrightarrow{cd}$ and $overleftrightarrow{ba}$ □ $overleftrightarrow{ad}$ and $overleftrightarrow{ae}$ □ $overleftrightarrow{de}$ and $overleftrightarrow{ba}$

Explanation:

Step1: Recall parallel - line property in prism

In a triangular prism, parallel lines are those that lie in parallel planes or are part of the same rectangular face.

Step2: Analyze each option

• For $\overleftrightarrow{AD}$ and $\overleftrightarrow{BC}$: They are opposite sides of a rectangular face, so they are parallel.
• For $\overleftrightarrow{CD}$ and $\overleftrightarrow{BA}$: They are not parallel as they are non - parallel edges of the prism.
• For $\overleftrightarrow{AD}$ and $\overleftrightarrow{AE}$: They intersect at point $A$, so they are not parallel.
• For $\overleftrightarrow{DE}$ and $\overleftrightarrow{BA}$: They are not parallel as they are non - parallel edges of the prism.

Answer:

$\overleftrightarrow{AD}$ and $\overleftrightarrow{BC}$