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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
Hi David,
  Unless I have misread you, I think you have answered Cynthia's original
question rather than my "follow-up 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
coordinate-based argument I had in mind.

cheers,
     Alan

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