Trapezoid Mid-Segment: 2 Discoveries

Recall that a MID-SEGMENT (or Median) of a trapezoid is a segment that connects the midpoints of its 2 non-base sides.   Interact with the applet below for a few minutes.   Be sure to change the locations of the trapezoid's VERTICES lots of times! What 2 conclusions can you make about the mid-segment of any trapezoid?  
Construct a valid 2-column, paragraph, or coordinate geometry proof to prove each conclusion true.