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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: patb Date: Apr 21 2008
you might re-examine item 3.  It is easy to prove that a rhombus has
perpendicular diagonals...

Whether a kite is a rhombus depends on a single element of the definition.  Some
people define a kite as having two pairs of adjacent sides, and others that
there be two distinct pairs.  If the requirement is for two distinct pairs, then
a rhombus is NOT a kite.
I prefer the inclusive definition, but you see the same kind of thing in some
books for a trapazoid (exactly one pair of parallel sides verses at least one
pair of parallel sides, making parallelograms a subset of trapazoids...)
some history that might be of interest here...
http://www.pballew.net/arithme5.html #kite

Pat

On Apr 20 2008, Jonsonian wrote:
> The criteria for a kite are
1. It is a quadrilateral
2. two pairs
> of adjacent sides equal
3. The diagonals cut each other or
> intersect at 90 degrees
A rhombus fails on the third count so it is
> not a kite
A square is a special type of kite just as a square is a
> special type of a rectangle but a rectangle is not necessarily a
> square and a kite is not necessarily a square.
From this definition
> there need not be any isosceles triangle obtained by drawing the
> diagonals of a kite. this means that a "delta" shaped object with
> our sides is a kite

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