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Thread: Quadrilateral Family: In nice and green valley there is a building with 4 floors...

  1. #11
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    Quote Originally Posted by shahar View Post
    The flour need to accommodate by each 4-gon that have the unique properties that no others figure have.

    In the article(now when I read it again), the 4-gons that I mentioned are the extreme figure in the hierarchy in the 4-gons family.
    I repeat by the figures that in last in hierarchy.

    (the hierarchy tree)
    But why it so?!.... ?!
    I don't think the figures you listed can be put in any one "correct" order. There are multiple ways to make a tree, depending on the properties you consider first. You could say that the square is a kind of rhombus, and the rhombus is a kind of kite (if you use an inclusive definition); and if you are defining trapezoid in the British sense of having no parallel sides, you can say that the kite is a kind of trapezoid. But that is not the order you say they gave.

    If we focus on symmetry, the square has four lines of symmetry, the rhombus two, the kite one, and the trapezoid none, so this results in the same order.

    I am wondering if it is really intended to be just a discussion-starter, rather than a problem with one correct answer. I couldn't translate the PDF you provided, but in part it looked like a discussion of teaching, which may have been focused on how to discuss such questions.

  2. #12
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    Quote Originally Posted by shahar View Post
    The flour need to accommodate by each 4-gon that have the unique properties that no others figure have.
    In the article(now when I read it again), the 4-gons that I mentioned are the extreme figure in the hierarchy in the 4-gons family.
    I repeat by the figures that in last in hierarchy.
    (the hierarchy tree) But why it so?!.... ?!
    I find this to be a rather odd discussion. That is because the trapezoid seems to be the odd figure out.
    Although the trapezoid is a quadrilateral like the other three the relation stops there.
    For each of the kite, the rhombus , & the square all have two pair of congruent sides, they have perpendicular diagonals.
    Moreover the square is a special case of rhombus.
    Perhaps, if it were an isosceles trapezoid the problem is more coherent.
    “A professor is someone who talks in someone else’s sleep”
    W.H. Auden

  3. #13
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    I'll take the one that's cheapest to rent
    I'm a man of few words...but I use 'em often!!

  4. #14
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    Quote Originally Posted by Denis View Post
    I'll take the one that's cheapest to rent
    I already told you that the cheapest rent for you is the (street) corner where you spend most of your time. Did you forget that already?
    I'm ready to buy your house. Do you take e-bills? I have many of those.
    A mathematician is a blind man in a dark room looking for a black cat which isn’t there. - Charles R. Darwin

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