Triangle ABC: Identifying the Median from Multiple Line Segments

Look at the triangles in the figure.

Which line is the median of triangle ABC?

To determine the median of triangle $ABC$, we need to identify the line that extends from one vertex to the midpoint of the opposite side.

• Step 1: Review the given line segments in the figure.
• Step 2: Recall that a median connects a vertex to the midpoint of the opposite side.
• Step 3: Examine each line in the context of $\triangle ABC$.

Let's consider each given line:

• Line $AF$ does not appear to connect to the midpoint of any side of the triangle directly.
• Line $DE$ is an internal line and does not serve as a median of the main triangle $ABC$.
• Line $FE$ is similar to $DE$, serving non-median purposes interior to another structure.
• Line $AG$ starts at vertex $A$ and extends to point $G$, lying on side $BC$. If $G$ is the midpoint of $BC$, then $AG$ qualifies as the median.

Verification: Point $G$ is positioned directly between points $B$ and $C$ along line $BC$, confirming its role as the midpoint.

Thus, the line $AG$ is indeed the median of triangle $ABC$ since it fulfills connecting vertex $A$ and the midpoint of side $BC$.

Therefore, the solution to the problem is $AG$ as the median of triangle $ABC$.