James King
Posts:
66
From:
University of Washington
Registered:
12/3/04


Re: Classification of quadrilaterals
Posted:
Dec 21, 1994 9:42 AM


I hold no brief for general trapezoids, but here are a couple of theorems.
Let ABCD be a trapezoid with AB  CD.
The two diagonals are concurrent with the line through the midpoints of the parallel sides.
(strictly speaking, this is a special case of a theorem in projective geometry, but so are many theorems about parallelograms)
The segment connecting the midpoints of AB and CD bisects the segment connecting the midpoints of BC and DA.
The segment connecting the midpoints of AB and CD divides the trapezoid into two pieces of equal area which are not congruent for the general trapezoid.
In perspective drawing of rectangles with sides parallel to the drawing plane, one ends up with trapezoids.
This is not exactly a ringing endorsement of trapezoids is it?
Jim King

