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Re: kites (fwd)
Posted:
Nov 13, 1997 3:10 PM


See addendum below.
 Forwarded message  Date: Thu, 13 Nov 1997 22:01:15 +0200 (SST) From: Mike de Villiers <mdevilli@pixie.udw.ac.za> To: "Eileen M. Klimick Schoaff" <SCHOAFEM@BUFFALOSTATE.EDU> Cc: geometryprecollege@forum.swarthmore.edu Subject: Re: kites
On Thu, 13 Nov 1997, Eileen M. Klimick Schoaff wrote:
> Just curious. Is there an official name for a nonconvex quadrilateral with > two pair of adjacent sides congruent, i.e., a kite that is nonconvex? 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 ADDENDUM: Although these names are descriptive, it is probably easiest to simply talk of convex and concave kites.
My > 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 > >



