1. The problem asks to identify the term that describes the segment $\overline{DF}$ in the given triangle. 2. Important definitions: - A **median** connects a vertex to the midpoint of the opposite side. - An **angle bisector** divides an angle into two equal angles. - A **perpendicular bisector** is a line perpendicular to a segment and passes through its midpoint. - An **altitude** is a perpendicular segment from a vertex to the line containing the opposite side. 3. From the description, $\overline{DF}$ is drawn from vertex $D$ to point $F$ on side $\overline{EG}$. 4. The right angle at $F$ indicates $\overline{DF}$ is perpendicular to $\overline{EG}$. 5. Since $\overline{DF}$ is perpendicular to $\overline{EG}$ and starts at vertex $D$, it fits the definition of an **altitude**. 6. There is no information that $F$ is the midpoint of $\overline{EG}$, so it is not necessarily a median or perpendicular bisector. 7. It is not an angle bisector because it does not split an angle at $D$. **Final answer:** $\overline{DF}$ is an **altitude**.