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Re: Kites: Are rhombuses kites?
Posted:
Nov 13, 1997 4:27 AM
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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
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