Triangle Median Identification: Locating the Correct Line Segment

Look at the triangle ABC below.

Which of the following lines is the median of the triangle?

To solve this problem, we apply the definition of a median in a triangle. A median is a line segment drawn from a vertex to the midpoint of the opposite side. In the diagram of the triangle ABC:

• Line $AD$ originates from vertex $A$ and is directed towards point $D$ on side $BC$.
• We need to check if $D$ is the midpoint of $BC$.
• Given that $AD$ meets the definition of a median by dividing $BC$ into two equal segments, it is indeed the median.

After evaluating the possible choices:

• Choice 1: $AD$ is a line from $A$ to the midpoint of $BC$.
• Choice 2: $AE$ doesn't bisect any side.
• Choice 3: $EC$ is not a median.
• Choice 4: $AC$ does not connect a vertex to a midpoint of the opposite side.

Therefore, the solution to the problem is that line segment AD is the median of triangle ABC.