Discussion:  All Topics in Geometry 
Topic:  Is a rhombus a kite? 
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Subject:  RE: Is a rhombus a kite? 
Author:  Mathman 
Date:  May 6 2005 
> I teach math coming from a physics background.
Me too. Both are the same at some point, the one the language of the other when
words are not enough.
> There is a simple demo that can be done with
> Geometer's Sketchpad where a trapezoid, parallelogram, rectangle,
> rhombus, square, and kite are all constructed and presented
> initially as squares. Overtly they are squares, but they behave
> differently when the vertices are dragged. It makes sense to name
> the shapes according to their behavior, so a square whose only
> invariant property, under distortion, is that one pair of opposite
> sides remains parallel, would be a trapezoid, etc.
This I like; the invariants under distortion. And GSP does have some uses.
As well, if a figure has all of the properties of another figure, they are of
the same set of figures. A square has all of the properties of the kite [and
the rhombus, and the parallelogram ....], so it is in turn one of each set by
definition of members of that set. There seems to be no argument that all four
sided figures are quadrilaterals even though there is a general quadrilateral
with none of the properties of the others except to have four sides.
David.
 
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