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Re: kites (fwd)
Posted:
Nov 13, 1997 3:10 PM
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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: geometry-pre-college@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 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
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
>
>
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