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Median of a Trapezoid Properties

Topic:
Trapezoid
Recall that a 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 median of any trapezoid?  
Construct a valid 2-column, paragraph, or coordinate geometry proof to prove each conclusion true.