Question

1. which line segment could be a midsegment of \\( \triangle a b c \\)?

Explanation:

Step1: Recall the definition of a midsegment

A midsegment of a triangle is a segment that connects the midpoints of two sides of the triangle.

Step2: Analyze each option

• $\overline{AF}$: It is a median (connects a vertex to the mid - point of the opposite side), not a midsegment.
• $\overline{DC}$: Connects a vertex ($D$) and a non - midpoint on another side (assuming $D$ is a mid - point of $AB$, but $C$ is a vertex, not a mid - point of another side).
• $\overline{BG}$: Connects a vertex ($B$) and a point ($G$) which is the centroid (intersection of medians), not a midsegment.
• $\overline{DE}$: If $D$ is the mid - point of $AB$ and $E$ is the mid - point of $AC$, then by the definition of a midsegment (connects midpoints of two sides of a triangle), $\overline{DE}$ is a midsegment of $\triangle ABC$.

Answer:

$\overline{DE}$