The segment that is parallel to $\overline{CD}$ in the given diagram is $\overline{AB}$.

This is because $\overline{AB}$ and $\overline{CD}$ are opposite sides of the rectangle $ABCD$, which ensures they are parallel to each other by the properties of rectangles.

Would you like further details on the geometric properties of this figure or have any other questions?

Here are some related questions for further exploration:

1. What are the properties of a rectangle that ensure opposite sides are parallel?
2. How do you prove two line segments are parallel in a geometric figure?
3. What is the significance of point $F$ in this diagram?
4. How can you calculate the length of a diagonal in a rectangle, like $\overline{AC}$?
5. How does the altitude from $C$ to the base $\overline{AB}$ affect the properties of this shape?

Tip: Parallel lines always maintain a constant distance and never intersect, which is one of their key defining properties.