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 Discussion: All Topics 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: Annie Date: Dec 13 2004
On Dec 13 2004, Mathman wrote:
> Again, so far as I know, a figure is one
> defined if it has ALL of the properties of the defined figure, "ALL"
> meaning those necessary and sufficient as fit its formal
> description.  Why not consider the parallelogram as a general
> trapezoid having one non-parallel side move towards parallelism with
> the the other?  Then, as with the definition of limit, there is no
> distinction in the limit. This is a finite limit of slope, not such
> a thing as a circle becoming a line "at infinity".

I tend to agree with you, as it's an argument that makes the most sense to me
and allows the most connections between the different quadrilaterals.  But the
fact remains that many American high school geometry texts use the less
inclusive definition.  Is it a parallelogram?  Yes.  Well, then it can't be a
trapezoid any more.

So getting back to Cynthia's most recent questions, does anyone know the history
of when or why the less inclusive definition came to be used in schools, at
least in the US? Is the more inclusive definition used in other countries in
current K-12 textbooks?

My geometry textbook collection only dates back to an early 1960s Mary P.
Dolciani Geometry text, in which a parallelogram is decidedly NOT a
trapezoid.

A past thread on this in the geometry.pre-college newsgroup is

http://mathforum.org/epigone/geometry-pre-college/23

though it doesn't specifically answer Cynthia's question of when this
happened.

-Annie