A is true as it is pretty much the definition of a median.
B is true and can be demonstrated with a trapezoid's area.
If you were to draw a median (see definition above) on a trapezoid, cut the pieces in half, and then match up one of the sides, you would get a parallelogram!
(see attached)
C is true. You can prove it in a similar fashion to the midline theorem.
D is not true, of course, because it directly contradicts A.
