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Topic: Kites: Are rhombuses kites?
Replies: 26   Last Post: Aug 29, 2002 11:49 AM

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 Mike de Villiers Posts: 38 Registered: 12/6/04
Re: Kites: Are rhombuses kites?
Posted: Nov 13, 1997 4:27 AM

On 10 Nov 1997, David Rome wrote:

> I am having a spirited discussion with a colleage as to whether or not
> the definition of a kite allows it to be considered to be a rhombus.
> The general definition of a kite is a quadrilateral with two sets of
> consecutive congruent disjoint sides. The question is: what is meant
> by disjoint? Different length, or just separatable at the vertices?
> My colleague maintains that a rhombus cannot be a kite, since all its
> sides are congruent, thus, non-disjoint. Some material I have seen,
> including venn diagrams of parallelograms, includes kites as rhombuses
> when both sets of sides are congruent. What do you think?
>

It depends on one's definition - a better way of defining the kites is to
say that a kite is any quad with (at least one) axis of symmetry through a
pair of opposite angles. If one CHOOSES this definition, then obviously a
rhombus is included.
But if one CHOOSES to define a kite say as any quad with ONLY ONE axis of
symmetry through a pair of oopposite angles, then a rhombus is NOT
included. It is all a matter of choice. Normally we prefer the INCLUSIVE
definitions since any theorems that we prove for kites will then
automatically also apply to rhombi - so there is no need to prove them again!

Michael de Villiers
Univ Durban-Westville

Date Subject Author
11/10/97 David Rome
11/10/97 Guy F. Brandenburg
11/12/97 Michael Keyton
11/11/97 Joshua Zucker
11/11/97 Gary Tupper
11/11/97 Guy F. Brandenburg
11/12/97 Michael Keyton
11/12/97 Joshua Zucker
11/11/97 John Conway
11/13/97 Mike de Villiers
11/11/97 John Conway
11/11/97 Joshua Zucker
11/11/97 John Conway
11/11/97 Michael Keyton
11/11/97 John Conway
11/11/97 Eileen M. Klimick Schoaff
11/11/97 Joshua Zucker
11/13/97 Mike de Villiers
11/11/97 Michael Keyton
11/11/97 Eileen M. Klimick Schoaff
11/12/97 Michael Keyton
11/13/97 Mike de Villiers
8/28/02 Diane
8/29/02 Walter Whiteley
8/29/02 Nat Silver
8/29/02 RFincutter@aol.com
8/29/02 John Conway