In the given diagram of a rectangular prism, we need to determine which lines are parallel.

A rectangular prism is a 3D shape with opposite faces that are rectangles, and corresponding edges (lines) that are parallel. Let's examine the options:

1. Line $\overline{KO}$ and Line $\overline{LO}$:

   • $KO$ is a vertical edge of the prism.
   • $LO$ is a horizontal edge of the base of the prism.
   • These two edges are not parallel; they are perpendicular to each other.

2. Line $\overline{HI}$ and Line $\overline{HK}$:

   • $HI$ and $HK$ are adjacent edges of the top face of the prism.
   • These two lines are not parallel; they are perpendicular.

3. Line $\overline{IM}$ and Line $\overline{KO}$:

   • $IM$ is a vertical edge on the front right of the prism.
   • $KO$ is a vertical edge on the back left of the prism.
   • These two lines are parallel because they run in the same direction and are part of the vertical edges of the prism.

4. Line $\overline{IJ}$ and Line $\overline{HL}$:

   • $IJ$ is a horizontal edge on the right face of the prism.
   • $HL$ is a diagonal line from the top left corner to the bottom left.
   • These two lines are not parallel.

Thus, the correct pair of parallel lines is $\overline{IM}$ and $\overline{KO}$.

Would you like more details on the reasoning or have any other questions?

5 Relative Questions:

1. What are the properties of parallel lines in three-dimensional shapes?
2. How can you determine if two lines are perpendicular or parallel in a rectangular prism?
3. Why are vertical edges of a rectangular prism always parallel to each other?
4. Can two lines be parallel if they lie on different planes? Why or why not?
5. How would the analysis change if the prism were a cube instead of a rectangular prism?

Tip:

When identifying parallel lines in a 3D figure, look for edges that run in the same direction and do not intersect, even if they are on different faces.