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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 5 2005
On May  5 2005, Susan wrote:
> I know we had a big discussion about parallelograms, but now I need
> help.  Some textbooks (especially the older ones) have rhombii as a
> subset of kites, but the newer ones do not.  It seems like the way
> you develop the area formulas make them related. Is a rhomus a kite?
> Is a square a kite?   Any ideas?  Has it changed over the years, or
> is it just me?

Everything depends upon definition.  "Kite" is a relatively new [and useful]
definition of an object.  If you define it as a four-sided figure in which two
adjacent sides are equal to each other, and the other two sides are also equal
to each other, and leave it at that,then both the rhombus and the square would
fit into the definition.  In the sense of "All cows eat grass, but not all grass
is eaten by cows.", the latter two fit also into other definitions such as the
already harried parallelogram, but the entire set of parallelograms does not fit
the definition of a "kite".  None the less, these two fit this definition of a
kite, and so are also kites.

David.

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