Question

1. which segment is parallel to (overline{df})?

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 \(AD = DB\)) and \(F\) is the midpoint of \(BC\) (since \(BF=FC\)). The segment \(DF\) is a mid - segment of triangle \(ABC\).

Step3: Determine the parallel segment

By the mid - segment theorem, the mid - segment \(DF\) is parallel to the side \(AC\) of triangle \(ABC\).

Answer:

\(\overline{AC}\)