Triangle Median Identification: Locating the Correct Line Segment in ABC

The triangle ABC is shown below.

Which line segment is the median?

To solve this problem, we need to identify the median in triangle ABC:

• Step 1: Recall the definition of a median. A median is a line segment drawn from a vertex to the midpoint of the opposite side.
• Step 2: Begin by evaluating each line segment based on the definition.
• Step 3: Identify points on triangle ABC:
• AD is from A to a point on BC.
• BE is from B to a point on AC.
• FC is from F to a point on AB.
• Step 4: Determine if these points (D, E, F) are midpoints:
• Since BE connects B to E, and E is indicated to be the midpoint of segment AC (as shown), BE is the median.
• AD and FC, by visual inspection, do not connect to midpoints on BC or AB respectively.

Therefore, the line segment that represents the median is $BE$.

Thus, the correct answer is: BE