In the given triangular prism, we are tasked with identifying which pairs of lines are parallel.

Explanation:

A triangular prism has two triangular bases and three rectangular lateral faces. Lines that lie along opposite edges of the same face or corresponding edges of the triangular bases are parallel. Let’s examine the lines in the figure:

• $RT$ and $VW$: These are corresponding edges of the two triangular bases (upper triangle and lower triangle), so they are parallel.
• $TW$ and $VW$: These two lines are along different faces and are not parallel.
• $ST$ and $VW$: These lines do not lie in the same plane and are not parallel.
• $RT$ and $ST$: These two lines lie along the same triangular face, but they are adjacent and not parallel.

Conclusion:

The parallel pairs of lines are:

1. $RT$ and $VW$
2. $RT$ and $ST$

Would you like more details, or do you have any questions?

Here are five related questions to expand your understanding:

1. What are the properties of parallel lines in three-dimensional figures?
2. How can you determine if two lines in a triangular prism are skew?
3. What is the difference between parallel and skew lines in geometry?
4. How do corresponding edges of a prism relate to one another geometrically?
5. What defines a triangular prism compared to other types of prisms?

Tip: When visualizing three-dimensional shapes, it helps to draw the shape from multiple perspectives to better understand parallelism and other relationships between edges.