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Math Help - Regular Quadrilateral Proof

  1. #1
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    Regular Quadrilateral Proof

    Suppose that Quadrilateral ABCD has the property that (i) AD || BC and (ii) C and
    D are on the same side of AB. Then Quadrilateral ABCD is regular.

    This seems rather obvious, but I must have a proof of the above. Can someone show please. Thanks!!
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  2. #2
    Super Member TheChaz's Avatar
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    Quote Originally Posted by jzellt View Post
    Suppose that Quadrilateral ABCD has the property that (i) AD || BC and (ii) C and
    D are on the same side of AB. Then Quadrilateral ABCD is regular.

    This seems rather obvious, but I must have a proof of the above. Can someone show please. Thanks!!
    This seems rather obviously false to me... unless "on the same side" is more specific than I realize.

    Actually, would you care to elaborate on the meaning of "on the same side"? If we end up with a square based on this phrase, I sure would like to know its meaning...
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  3. #3
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    Take the line AB. Then, C and D must be on the same side of the line... I'm sure where the confusion is here. Maybe try drawing it out... Thanks
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  4. #4
    Super Member TheChaz's Avatar
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    Quote Originally Posted by jzellt View Post
    Take the line AB. Then, C and D must be on the same side of the line... I'm sure where the confusion is here. Maybe try drawing it out... Thanks
    I can draw a million such quadrilaterals that ARE NOT regular!

    Take A, B, C, D to be:
    (0, 0), (0, 1), (1, 1), and (2, 0) for example.

    Like you, I am not sure where the confusion is here, but I have a good guess...
    Last edited by TheChaz; May 1st 2011 at 09:18 PM. Reason: spelczecker
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  5. #5
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    You're right... Thanks. This is a propostion right out of my professors lecture notes and I was asked to prove it. I guess he made a mistake... Thanks again
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  6. #6
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    In my professor lecture notes, he states:
    The following says that trapezoids (defined using the American convention, as opposed to
    the British convention) are regular.
    Then, the proposition is stated. So I guess I still need a proof the proposition posted in my original post...
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  7. #7
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    Hello jzellt,
    To define a regular trapezoid or a parallelogram something more than two parallel lines is required. For example the two parallel line segments are equal . you must be leaving something out



    bjh
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