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Topic: Classification of quadrilaterals
Replies: 17   Last Post: Jan 11, 1995 6:43 AM

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James King

Posts: 66
From: University of Washington
Registered: 12/3/04
Re: Classification of quadrilaterals
Posted: Dec 21, 1994 9:42 AM
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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






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