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Topic: Midsegment of a rectangle?
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Subject:   RE: More on What is a Trapezoid
Author: Craig
Date: Jan 3 2005
On Dec 15 2004, Mathman wrote:

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.

The definition given for an isosceles trapezoid was "a trapezoid with congruent
legs."  Hence the theorem about congruent base angles, which can apply only in
the "exclusive" version of trapezoids:  If parallelograms are trapezoids, then,
since (whichever "base" you use) the legs are congruent, the parallelogram is an
isosceles trapezoid; the rectangle is the only parallelogram which would fit the
theorem about congruent base angles.

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