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Math Help - True or False

  1. #1
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    True or False

    If a theorem is proved using the Euclidean Parallel Postulate or its equivalence, then it is strictly Euclidean. True?

    Parallelograms only exist in Euclidean Geometry. False?

    A quadrilateral that is both Saccheri and Lambert is a rectangle. False?
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  2. #2
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    "Parallelograms only exist in Euclidean Geometry. False?"

    No, true because the sum of the angles in other geometries are either more or less than 360 degrees.
    Last edited by wonderboy1953; July 9th 2010 at 01:09 PM. Reason: correction
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  3. #3
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    But I thought a Saccheri Quadrilateral is a parallelogram in hyperbolic geometry?
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  4. #4
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    Maybe I'm being too restrictive. Anyways I found this for you through a Google search:

    http://public.csusm.edu/aitken_html/m410/quad.pdf
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  5. #5
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    Quote Originally Posted by MATNTRNG View Post
    But I thought a Saccheri Quadrilateral is a parallelogram in hyperbolic geometry?
    Then what do you mean by "parallelogram"? Or, for that matter, by "a parallel"? If you take any two non-intersecting lines to be "parallel", then, yes, a Saccheri Quadrilateral is a parallelogram. But many texts make a distinction between "parallel lines" (limiting parallels in other books) and "non-intersecting lines". Opposite sides of a Saccheri quadrilateral are non-intersecting lines.
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