In this problem, we are asked to determine which segment is not skew to segment $\overline{EK}$. Segments are considered skew if they are neither parallel nor do they intersect. To find the answer, we need to analyze each segment given in the choices and compare it to $\overline{EK}$.

Segments to consider:

• CI
• AB
• LG
• FA

Let's evaluate them one by one:

1. Segment CI: $\overline{CI}$ is on the opposite face of the prism compared to $\overline{EK}$, and these two lines do not intersect and are not parallel, making them skew.

2. Segment AB: $\overline{AB}$ lies at the bottom of the prism and is neither parallel nor intersects with $\overline{EK}$, so they are skew.

3. Segment LG: $\overline{LG}$ connects points on the same face of the prism as $\overline{EK}$ and is part of the same diagonal structure. Therefore, $\overline{LG}$ and $\overline{EK}$ intersect at point L, meaning they are not skew.

4. Segment FA: $\overline{FA}$ lies on a completely different face, does not intersect $\overline{EK}$, and is not parallel, making it skew.

Conclusion:

The segment that is not skew to $\overline{EK}$ is $\overline{LG}$.

Would you like further details or explanations about skew lines or related geometric concepts?

Here are 5 related questions to expand on this topic:

1. What are the properties of skew lines in 3D geometry?
2. How do you determine if two segments are parallel in 3D space?
3. Can two lines be both skew and perpendicular?
4. What is the difference between intersecting lines and concurrent lines?
5. How do we find the angle between two skew lines?

Tip: When determining if two lines are skew, always check if they are in parallel planes or intersect at any point.