Triangle ABC: Identifying the Side with Coinciding Median and Height

To solve this problem, we need to use the properties of medians and heights, specifically in isosceles triangles. In an isosceles triangle, the median from the vertex angle to the base is also the height. In the diagram of triangle ABC, given the problem context and a typical configuration of an isosceles triangle, we can see that:

• The side AB is horizontally aligned in the diagram.
• The point D, directly below A, suggests that the median from A also serves as the height to the base BC, if AB = BC making triangle ABC isosceles.

Therefore, in triangle ABC, side AB is both the median and the height of the triangle, assuming a vertical symmetry along median AD, characteristic of an isosceles triangle configuration.

Therefore, the correct answer is $AB$.