Discussion:  Dynamic Geometry Exploration: Properties of the Midsegment of a Trapezoid tool 
Topic:  Midsegment of a rectangle? 
Related Item:  http://mathforum.org/mathtools/tool/15621/ 
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Subject:  RE: Midsegment of a rectangle? 
Author:  Alan Cooper 
Date:  Dec 8 2004 
Is it possible to find *any* nontrapezoidal example of a quadrilateral for
which the distance between the midpoints of two nonadjacent sides is equal to
the average of the lengths of the other two sides?
Alan
P.S. I am firmly in the camp of those who consider parallelograms to be
trapezoidal so I wouldn't consider a parallelogram or rectangle to be examples
of what I am asking for.
 
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