Triangle Median Construction: Identifying the Line from Vertex to Midpoint

ABC is a triangle.

What is the median of the triangle?

To solve the problem of identifying the median of triangle $\triangle ABC$, we follow these steps:

• Step 1: Understand the Definition - A median of a triangle is a line segment that extends from a vertex to the midpoint of the opposite side.
• Step 2: Identify Potential Medians - Examine segments from each vertex to the opposite side. The diagram labels these connections.
• Step 3: Confirm the Median - Specifically check the segment EC in the context of the line segment from vertex $E$ to the side $AC$, and verify it reaches the midpoint of side $AC$.
• Step 4: Verify Against Options - Given choices allow us to consider which point-to-point connection adheres to our criterion for a median. EC is given as one of the choices.

Observation shows: From point $E$ (assumed from the label and position) that line extends directly to point $C$—a crucial diagonal opposite from considered midpoint indications, suggesting it cuts $AC$ evenly, classifying it as a median.

Upon reviewing the given choices, we see that segment $EC$ is listed. Confirming that $EC$ indeed meets at $C$, the midpoint of $AC$, validates that it is a true median.

Therefore, the correct median of $\triangle ABC$ is the segment $EC$.