Question

in the triangular prism shown below, which lines are parallel? wy and tv, xy and tw, wy and vy, uv and wx

Explanation:

Step1: Recall parallel - line property in prism

In a triangular prism, parallel lines are those that lie in parallel planes and do not intersect.

Step2: Analyze each option

• For $\overrightarrow{WY}$ and $\overrightarrow{TV}$: They are not parallel as they are in non - parallel planes and their directions are different.
• For $\overrightarrow{XY}$ and $\overrightarrow{TW}$: In a triangular prism, the corresponding edges of the parallel bases are parallel. The bottom - base edges and the top - base edges which are in parallel planes and have the same direction are parallel. $\overrightarrow{XY}$ and $\overrightarrow{TW}$ are such corresponding edges of the parallel bases.
• For $\overrightarrow{WY}$ and $\overrightarrow{VY}$: They share a common point $Y$, so they are not parallel.
• For $\overrightarrow{UV}$ and $\overrightarrow{WX}$: They are in non - parallel planes and do not have the same direction, so they are not parallel.

Answer:

$\overrightarrow{XY}$ and $\overrightarrow{TW}$