
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, nondisjoint. 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 DurbanWestville

