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 Discussion: All Topics Topic: Midsegment of a rectangle? Related Item: http://mathforum.org/mathtools/tool/15621/

 Post a new topic to the tool: Dynamic Geometry Exploration: Properties of the Midsegment of a Trapezoid discussion
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 Subject: RE: More on What is a Trapezoid Author: The Math Guy Date: Dec 13 2004
About 12 years ago, I struggled with both of these definitions.  Is the
trapezoid a separate line in the quadrilateral family or is it related, some
how, to the parallelogram.  Does the kite stand alone or is it linked.  I, long
ago, figured out that it was ok for an equilateral triangle to be considered to
be isosceles as well - an isosceles triangle having at least two sides
congruent.  So after some extensive questioning of minds greater than mine, I
came to believe that a square was both a rectangle and a rhombus - the square
has all of the properties of both the rectangle and the rhombus.  So, why can't
a rectangle have all of the properties of both the parallelogram and the
isosceles trapezoid?  Or a Rhombus have all of the properteis of the
parallelogram and the kite?   Or for that matter, why can't a kite come from
both the family of congruent pairs of consecutive sides and the family of
perpendicular diagonals.  When we look at the symmetries of each of the
different families, it starts to make sense.