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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 13 2004
Another quick note:

I believe,and hy I've stuck wit hit, that the definition depends greatly on what
is required [again the necessary and sufficient conditions] in order to state in
an unqualified fashion what something *is.

If, in some drawing with quantities given, I see a figure and can state that it
is a quadrilateral with two sides parallel.  That is necessary and sufficient to
say that it must then be a trapezoid.

If I see a figure and can show that it is a parallelogram and one angle is a
right angle, that is necessary and sufficient to state that it is a
rectangle.

If I see a figure and can show that it is a parallelogram and its diagonals are
equal, then again it is a rectangle.  ...There is sometimes more than one way to
define an object, as with the square and the rhombus.  Either way, the
definition depends entirely on the minimal [sufficient] properties to
distinguish it from any lesser object [one with necessary, but not sufficient
properties for the purpose.]  That, to me, is what a "definition" is all about.
A chair or a seat; if they have the same definition, they are the same kind of
object, even if different in other ways.

David.