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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
On May  6 2005, David Chandler wrote:
> 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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