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Re: kites
Posted:
Nov 13, 1997 3:07 PM


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? 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.) Not seen this result before  nice! The duality suggests that similar result holds between cyclic and circum quads  check it out and let us know! Michael de Villiers
> > 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 > >



