If one of the bases is zero length, the result is a triangle. and is identical to the
triangle midsegment case.
The median line will then be half the remaining base. Try this out in the figure above by moving A to overlap B.

The median line is halfway between the bases. Adjust the trapezoid above by dragging any vertex and convince yourself this is so.

The median divides the trapezoid into two smaller trapezoids each with half the altitude of the original.