Triangle Height vs Median: Identifying Key Line Segments in ABC Triangle

To solve this problem, we need to correctly identify the height and median in the triangle $ABC$.

• Step 1: Understand the Definitions
  The height (or altitude) from a vertex of a triangle is a segment that is perpendicular to the line containing the opposite side. The median from a vertex is a segment that joins the vertex to the midpoint of the opposite side.
• Step 2: Apply Definitions to Diagram
  - Line $AB$ connects vertex $A$ to vertex $B$, forming a perpendicular segment to base $BC$. Hence, it is a height.
  - Line $EB$ connects vertex $A$ to point $E$, the midpoint, dividing segment $BC$ into two equal parts, thus acting as a median.
• Step 3: Match to Answer Choices
  Having sorted the segments as the height and the median, match our findings to the provided choices. The choice indicating that $BC + AB$ is the height and $EB$ is the median is correct.

Therefore, the solution to the problem is $BC + AB =$ height, $EB =$ median.