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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:   Midsegment of a rectangle?
Author: lanius
Date: Dec 8 2004
Hello,
Check out the highlighted tool on http://mathforum.org/mathtools
( http://mathforum.org/mathtools/tool/15621/ )It's a really nice Java applet that
explores the midsegment of a Traqezoid. I was playing with this and started
wondering, does this also hold for a rectangle? Does it hold for all
parallelograms? Does it hold for all convex quadrilaterals?

I remember having discussions with mathematicians that trapezoids should include
the family of parallelograms. Do you agree? Then should it also include the
family of triangles (given the applet at the bottom of the page)

What would be gained by defining trapezoids as quadrilaterals with *at least*
one pair of opposite sides parallel? What is lost? And similarly, what is gained
by defining trapezoids as quadrilaterals with *exactly* one pair of opposite
sides parallel. What is lost? Isn't this how K-12 textbooks currently define
trapezoid?

Thanks,
cynthia

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