Question

in the triangular prism shown below, which lines are parallel? select all that apply.

Explanation:

Step1: Recall the definition of parallel lines

Parallel lines are lines in a plane that do not intersect. In a triangular prism, we can use the properties of the prism's faces and edges.

Step2: Analyze each pair

• For \(\overleftrightarrow{RU}\) and \(\overleftrightarrow{TW}\):
• By the structure of the triangular prism, these lines are parallel as they are corresponding edges of the parallel faces.
• For \(\overleftrightarrow{ST}\) and \(\overleftrightarrow{VW}\):
• Similarly, they are parallel due to the prism's structure.
• For \(\overleftrightarrow{RU}\) and \(\overleftrightarrow{UW}\):
• These lines are not parallel as they intersect at point \(U\).
• For \(\overleftrightarrow{SV}\) and \(\overleftrightarrow{TW}\):
• They are parallel as per the prism's edge - face relationships.

Answer:

\(\overleftrightarrow{RU}\) and \(\overleftrightarrow{TW}\), \(\overleftrightarrow{ST}\) and \(\overleftrightarrow{VW}\), \(\overleftrightarrow{SV}\) and \(\overleftrightarrow{TW}\)