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 9 2004 
Unless I have misread you, I think you have answered Cynthia's original
question rather than my "followup question".
Cynthia asked whether the average length property holds for *all*
quadrilaterals, and my question was whether there *exist* any (other than
trapezoids). In other words, "part(b)" could be rephrased as "If the midsegment
satisfies the average length property, *must* the edges that it separates be
parallel?"
Interestingly, your "two triangles" construction does lead (after a couple more
lines of argument)to a proof that the answer to part (b) is "Yes" (in terms of
the second phrasing)  and that proof is much nicer than the
coordinatebased argument I had in mind.
cheers,
Alan
 
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