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Topic: kites
Replies: 5   Last Post: Nov 14, 1997 2:46 PM

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Mike de Villiers

Posts: 38
Registered: 12/6/04
Re: kites
Posted: Nov 13, 1997 3:01 PM
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On Thu, 13 Nov 1997, Eileen M. Klimick Schoaff wrote:

> Just curious. Is there an official name for a non-convex quadrilateral with
> two pair of adjacent sides congruent, i.e., a kite that is non-convex?

I don't think there is an "official" name - names that appear in SA
textbooks are "arrowheads" or "darts" which I rather like.
Michael de Villiers
> students have named them the StarTrek insignia, the Pontiac symbol, and the
> concave kite. We do an exercise found in the old Geometric Supposer manual
> where you reflect the point of intersection of the diagonals across the four
> sides of a quadrilateral and then determine the relationship between the
> resulting quadrilateral and the original. Squares produce squares,
> parallelograms produce parallelograms, rectangles produce rhombi and vice
> versa, kites produce isosceles trapezoids that are not parallelograms (unless
> the kite is a square) and vice versa most of the time (sometimes the kite is
> not convex). The key is the relationship of the diagonals in the original
> figure. The vertex angles of the new quadrilateral are equal to the angles
> formed by the diagonals of the original quadrilateral. And the vertex angles
> of the original quadrilateral are equal to the angles formed by the diagonals
> of the new quadrilateral. (I have not seen this proof in any textbook, but one
> of my undergraduate students proved it a few years ago.)
> So what do you call that thing? Essentially, one of the vertices of a convex
> kite is reflected across the shorter diagonal.
> Eileen Schoaff
> Buffalo State College

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