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Thread: How-to Questions

  1. #1
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    How-to Questions

    How do you construct a trapezoid that isn't a parallelogram?

  2. #2

    How-to Construct A Trapezoid that's NOT a Parallelogram

    Here is one possible way to do this trapezoid construction.

    Last edited by Kgreenhaus; 11-18-2010 at 05:43 AM.

  3. #3
    That's great that you can embed a video in a forum post. Good to know! Karen, you should post your video as a How-To on the main page.

  4. #4
    How to, indeed! And how do you construct it so that it doesn't degenerate into a triangle when you do the drag test? ... or a bow-tie? (which is the classic mistake of most beginners). Oh, and one more thing... It has to pass the drag test such that all possible configurations are represented. The most common mistake, if you get to this point, is making a trapezoid whose sides are of a fixed ratio.

    I present this question as an extension to the TGS classes I moderate, and I get some very creative solutions. I've posted them, along with several of my own, and some of the problematic trapezoids I've seen, along with several of the build instructions, etc... in the exchange under the title "Trapezoids." Please let me know what you think!

  5. #5
    Great post! Those different constructions could generate great discussions about the definition of trapezoid and the properties that result from different definitions.

  6. #6
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    Quote Originally Posted by M.Vasicek View Post
    I've posted them, along with several of my own, and some of the problematic trapezoids I've seen, along with several of the build instructions, etc... in the exchange under the title "Trapezoids." Please let me know what you think!
    Here is the link: http://sketchexchange.keypress.com/s...-the-trapezoid

    Thanks!
    Last edited by ams20518; 11-18-2010 at 11:46 AM. Reason: added link

  7. #7
    The fact that it is 'tricky' and one virtually has to resort to 'cheating' in order to construct a trapezoid so that it can't be dragged into a parallelogram would suggest the more sensible choice is to regard parallelograms as special cases of trapezoids. After all, parallelograms have ALL the properties of a trapezoid, just like a square has all the properties of a rectangle. More-over, just as one then doesn't have to again prove the properties of a rectangle which a square inherits from it, the same deductive economy applies if we consider parallelograms as trapezoids: all the trapezoid theorems immediately apply to parallelograms!

    Though not mathematically incorrect to define a trapezoid so as to exclude parallelograms, it is not deductively economical to do so, just as we today PREFER for economical reasons to regard squares as rectangles, even though Euclid himself defined rectangles as those 'oblong' quadrilaterals: "which are right-angled but not equilateral"! This shows that definitions in mathematics are often a matter of choice, and we usually choose them for convenience!

    Also have a look at my Hierarchical Quadrilateral Tree sketch at http://sketchexchange.keypress.com/s...rilateral-tree

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