Triangle Median Identification: Line Segment Analysis in ABC Triangle

Question

Look at the triangle ABC below.

Which of the line segments is the median?

AAABBBCCCGGGHHHFFFDDDEEE

Step-by-Step Solution

To identify the median in triangle ABCABC, we will utilize the definition of a median: it is the line segment extending from a vertex of the triangle to the midpoint of the opposite side.

In the diagram, triangle ABCABC is formed with vertices AA, BB, and CC. We need to identify which of the segments is drawn from a vertex and intersects the opposite side at its midpoint.

Examine segment FCFC:

  • FF appears to be a midpoint of side ABAB of the triangle ABCABC.
  • Line segment FCFC originates from vertex CC and extends to FF.

The segment FCFC meets the criteria for a median as it connects vertex CC to the midpoint of ABAB.

Therefore, we conclude that the median of triangle ABCABC is FC.

Answer

FC