> 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!