Calculate Triangle Height: Finding Altitude AD in Triangle ABC

To solve this problem, we need to identify the height of triangle ABC from the diagram. The height of a triangle is defined as the perpendicular line segment from a vertex to the opposite side, or to the line containing the opposite side.

In the given diagram:

• $A$ is the vertex from which the height is drawn.
• The base $BC$ is a horizontal line lying on the same level.
• $AD$ is the line segment originating from point $A$ and is perpendicular to $BC$.

The perpendicularity of $AD$ to $BC$ is illustrated by the right angle symbol at point $D$. This establishes $AD$ as the height of the triangle ABC.

Considering the options provided, the line segment that represents the height of the triangle ABC is indeed $AD$.

Therefore, the correct choice is: $AD$.