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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: More on What is a Trapezoid
Author: Mathman
Date: Dec 15 2004
On Dec 14 2004, Craig wrote:
> I haven't entered the fray on this topic, but let me tell you I have
> thoroughly enjoyed the back-and-forth.  I really like having
> discussions of this sort with my students (high school, mostly
> gifted).  

By the way, I'm firmly planted in the "inclusive"
> camp, even though the Geometry text we use (Jurgenson-Brown-
> Jurgenson) uses "exactly one pair" in its definition.  I guess they
> have to: they go on and on about isosceles trapezoids, giving a
> theorem that base angles are congruent in isosceles trapezoids.  If
> you use the inclusive definition of trapezoid, any parallelogram
> would be an isosceles trapezoid, which would disprove their nice
> theorem (unless you re-define isosceles trapezoids as those with
> congruent base angles, then make the theorem about proving the legs
> of an isosceles trapezoid are congruent).

Sorry, but how do your reach that conclusion?  An Isosceles trapezoid [although
I've never heard the term applied to other than the triangle], isn't *any*
trapezoid, but one in particular, as the square isn't any rectangle, but one in
particular.  If by Isosceles trapezoid you mean one with base angles equal, "any
parallelogram" does not have two base angles equal, but only the "rectangular
parallelogram" has that property.  So all rectangles would be "isosceles
trapezoids", but not all parallelograms.

David.

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