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

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kirby urner

Posts: 3,690
Registered: 11/29/05
Re: Based on the quadrilateral tree
Posted: May 1, 2013 11:57 PM
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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
(second from last example)

This source makes it clear that the inclusive definition is favored in
some circles.

This inclusive definition does allow us to speak of parallelograms
as a subspecies of trapezoid.


On Wed, May 1, 2013 at 1:57 PM, Dongwahn Suh <> 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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