Question

1. which segment is parallel to \\( \overline { f e } \\)?

Explanation:

Step1: Recall the mid - segment theorem

The mid - segment theorem states that the segment connecting the midpoints of two sides of a triangle is parallel to the third side.

Step2: Analyze the given triangle

In triangle \(ABC\), \(D\) is the midpoint of \(AB\) (since \(AD = DB\)), \(E\) is the midpoint of \(AC\) (since \(AE=EC\)), and \(F\) is the midpoint of \(BC\) (since \(BF = FC\)).
The segment \(DE\) connects the midpoints \(D\) and \(E\) of sides \(AB\) and \(AC\) respectively. But we are looking at the relationship for \(FE\).
The segment \(FE\) connects the midpoints \(F\) and \(E\) of sides \(BC\) and \(AC\) respectively.
The segment \(DF\) connects the midpoints \(D\) and \(F\) of sides \(AB\) and \(BC\) respectively. By the mid - segment theorem, \(DF\parallel AC\), \(FE\parallel AB\), \(DE\parallel BC\).

Answer:

\(\overline{AB}\)