On 5/2/2013 1:48 PM, Wayne Bishop wrote: > But he is also right. Although favored in some circles, it is one of > those (rather few) situations where the inclusive definition is not > universal. In fact, I think the majority of us prefer his, exactly 1 > pair of parallel sides. Moreover, convictions border on the > religious. You know, God is on our side whichever side that is. > > Wayne I'm not sure how God fits in here, but:
if we define a trapezoid to be a quadrilateral with 2 (or more) parallel sides, then any property of a trapezoid will cascade down to parallograms, rectangles, squares & rhombi. The only such property I am aware of: the area of a trapezoid is the product of the distance between parallel sides, and the average length of the parallel sides. And this formula does indeed cascade down - even to a triangle if we view it as a degenerate with side length 0 at the vertex.
If there is a comparable advantage to using the restrictive definition, I do not know it.