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Math Help - Parallelograms.

  1. #1
    Junior Member
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    Parallelograms.

    You have, five parallelograms. Four of the parallelograms are rectangles and one is a rhombus. Further, if the rhombus is not a square, and at least two of the rectangles are squares, which of the following choice is true?
    A. No rhombus is a parallelogram.
    B. Exactly one rectangle is a rhombus.
    C. No rectangles are parallelograms.
    D. Each parallelogram is a rectangle.
    E. At least three of the parallelograms are rhombus.
    Last edited by mr fantastic; June 4th 2010 at 07:03 AM. Reason: Re-titled.
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  2. #2
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    Hello winsome
    Quote Originally Posted by winsome View Post
    You have, five parallelograms. Four of the parallelograms are rectangles and one is a rhombus. Further, if the rhombus is not a square, and at least two of the rectangles are squares, which of the following choice is true?
    A. No rhombus is a parallelogram.
    B. Exactly one rectangle is a rhombus.
    C. No rectangles are parallelograms.
    D. Each parallelogram is a rectangle.
    E. At least three of the parallelograms are rhombus.
    The only one that is true is E: three parallelograms that are known to be rhombuses are the one designated a rhombus and the two rectangles which are known to be squares.

    A and C are never true: every rhombus is a parallelogram and every rectangle is a parallelogram.

    B is false: at least two of the rectangles are squares, and hence are rhombuses.

    D is false: the rhombus is not a square, and hence it's not a rectangle either.

    Grandad
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