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 10 2004 
> A quick followup: I'm thinking of a quadrilateral with top and
> bottom of lengths "a" and "b". There is a line joining the
> midpoints of the two sides, and its length is given as (a+b)/2. You
> want proof that the top and bottom are parallel, [and the midpoint
> divider would then also be parallel to them.] Is this what you
> mean?
Yes.
And I think your triangle decomposition (by drawing in a diagonal) leads to a
very nice proof of this fact.
 
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