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Replies: 17   Last Post: Jan 11, 1995 6:43 AM

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 Chenteh Kenneth Fan Posts: 1 Registered: 12/10/04
Posted: Dec 21, 1994 5:06 PM

Yes, at least for convex quadrilaterals, it is true that if there
is one bisector segment which bisects the quadrilateral, then the

Sketch of proof:

Fix a line MM' (the besector segment), and draw AB with midpoint M.

Assume AB<= CD. Consider C'D' with midpoint M and length C'D'=length CD.

We ask when can area AC'M'M = area MM'D'B ?

Notice that area MM'A = area MM'B.

So equivalently, we ask when can area AM'C' = area BM'D' ?

In other words, when can the altitudes of the triangles AM'C' and BM'D'
as measured from the base on C'D' be equal? This occurs
when AB || C'D'.

I bet this can be modified to accomodate non-convex quadrilaterals too...
but alas! I've a plane to catch...darn! just when things are getting
interesting...

Happy Holidays everyone,
Ken

A C'

M M'

B D'

Date Subject Author
12/15/94 E7M2WAT@TOE.TOWSON.EDU
12/16/94 W Gary Martin
12/16/94 Henri Picciotto
12/17/94 John Conway
12/17/94 roitman@oberon.math.ukans.edu
12/18/94 John Conway
12/20/94 Chenteh Kenneth Fan
12/21/94 John Conway
12/21/94 Walter Whiteley
12/21/94 William T. Webber
12/21/94 James King
12/21/94 Chenteh Kenneth Fan
12/21/94 John Conway
12/21/94 John Conway
12/21/94 John Conway
12/21/94 Chenteh Kenneth Fan
12/21/94 Chenteh Kenneth Fan
1/11/95 joe malkevitch