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Geometry - Can a trapezoid ever be a kite, and vice versa?

  1. Feb 26, 2012 #1
    1. The problem statement, all variables and given/known data

    Can a trapezoid ever be a kite?
    Can a kite be a trapezoid?

    2. The attempt at a solution

    I believe that the answer to both is no.

    1. If a trapezoid was a kite, wouldn't the pair of parallel sides, along with the congruent consecutive sides, imply that it was a parallelogram? But a trapezoid only has one pair of parallel sides?

    2. If a kite was a trapezoid, then wouldn't it have two pairs of opposite congruent angles, rather than exactly one?

    I feel like my answers are correct, it's just that they don't seem mathematically sound. Any help is appreciated. :)
     
  2. jcsd
  3. Feb 27, 2012 #2

    ehild

    User Avatar
    Homework Helper
    Gold Member

    Read http://www.mathsisfun.com/quadrilaterals.html, and see the picture:

    quadrilateral-class.gif

    The definition of trapezoid does not say that the other sides can not be also parallel.

    Is square a trapezoid?

    The definition of kite does not say that the the other pair of opposite angles can not be also equal.

    Is square a kite?

    Are both quadrilaterals?

    ehild
     
    Last edited: Feb 28, 2012
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