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

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 John Conway Posts: 2,238 Registered: 12/3/04
Posted: Dec 21, 1994 4:29 PM

Ah yes, I see it IS all quadrilaterals (for which the segments
joining the midpoints of pairs of opposite sides meet) - for the
midpoint of (A+B)/2 and (C+D)/2 is (A+B+C+D)/4, the centroid of
the four vertices. So indeed in ANY quadrilateral these "bisector
segments" bisect each other. Nice try, though.

I don't regard the fact that the bisector segment from AB to CD
bisects the area as really different from the fact that the area
formula works for trapezoids. You're going to have a hard time
convincing me that trapezoids were really worth naming!

I wonder - if one bisector segment of a quadrilateral DOES
bisect it, is it necessarily a trapezoid? It feels as though
it might be.

John Conway

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