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Topic: Based on the quadrilateral tree
Replies: 14   Last Post: May 8, 2013 7:00 PM

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Wayne Bishop

Posts: 4,995
Registered: 12/6/04
Re: Based on the quadrilateral tree
Posted: May 2, 2013 4:48 PM
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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

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 <dsuh2@schools.nyc.gov> 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.




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