Verify if AD is the Height in Triangle ABC: Geometric Properties Analysis

To determine if AD is the height of triangle ABC, we start by recalling the definition of a height in a triangle. A height is a perpendicular line segment from a vertex to the line containing the opposite side. In triangle geometry, for AD to be considered a height, it must be perpendicular to the line BC.

The given diagram shows that AD is indeed perpendicular to BC, as denoted by the perpendicular symbol (the small square at the intersection indicating a $90^\circ$ angle). This matches the definition of a height in a triangle, which is a line drawn perpendicular from a vertex (in this case, vertex A) to the line containing the opposite side (here, BC).

Since AD meets this criterion of being perpendicular to the opposite side, we can conclusively state that AD is indeed the height of the triangle ABC. Thus, the statement "AD is the height in the triangle ABC" is true.

Therefore, the solution to the problem is True.