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.
At 08:57 PM 5/1/2013, kirby urner wrote: >Yes, parallelograms are quadrilaterals with both pairs of sides parallel, >meaning they include rhombi (all sides same length) and rectangles >(all angles same size). > >A square is a "rhombic rectangle". > >Trapezoids have at most one pair of parallel edges according to the >exclusive definition (versus "at least one"). > >The trapezoids we don't see so often are the ones where the base >angles are not both < 90 degrees, or both > 90 > >http://zonalandeducation.com/mmts/geometrySection/commonShapes/trapezoid/trapezoid.html >(second from last example) > >This source makes it clear that the inclusive definition is favored in >some circles. > >http://www.math.washington.edu/~king/coursedir/m444a00/syl/class/trapezoids/Trapezoids.html > >This inclusive definition does allow us to speak of parallelograms >as a subspecies of trapezoid. > >Kirby > >On Wed, May 1, 2013 at 1:57 PM, Dongwahn Suh <email@example.com> wrote: > > I remember teaching quadrilaterals and creating a tree diagram to > differentiate and connect the characteristics of > quadrilaterals. Stemming out of quadrilaterals, the parallelogram > then breaks up into rhombii and rectangles, which then combine to > form a square. The trapezoid drops down into its own stem and then > from the trapezoid was the special isosceles trapezoid. Since > parallelograms must have two pairs of parallel sides, the > trapezoid only has two parallel sides and no more. Otherwise we > would be able to categorize some trapezoids as parallelograms.