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Is a square a rhombus?

Discussion in 'Mathematics' started by lynnestartin, Jan 7, 2011.

  1. I always had the belief that a square was a special kind of rhombus, because a rhombus just needed to have 4 equal sides. But some of my schools have got maths dictionaries that say a rhombus cannot have angles of 90. Thoughts please?
  2. DM

    DM New commenter

  3. DM

    DM New commenter

  4. DM

    DM New commenter

    Oops double post (only one with correct spelling)!
  5. First post so will try to be careful...
    I would always think of a quadrilateral in terms of its diagonals - I would say that all of the other properties come as a consequence of the relationship between these. A rhombus only needs to have two diagonals that are perpendicularly bisecting. A square satisfies this - therefore a square is a rhombus.
    Similarly a parallelogram need only have bisecting diagonals. A rhombus satisfies this - therefore a rhombus is a parallelogram.
  6. adamcreen

    adamcreen Occasional commenter

    Squares are the only shapes in the intersection between the set of rhombi and the set of rectangles.

    Somewhere I have a Venn diagram picture of quadrilateral set relations but maybe there's an electronic version...
  7. tafkam

    tafkam Occasional commenter

    I do hope so, because I really want one, and the thought of getting my head round creating it electronically is making my brain ache already!
  8. tafkam

    tafkam Occasional commenter

  9. Maths_Mike

    Maths_Mike New commenter

    I dont see why people get so hung up about this.

    A square is NOT a rhombus its a square.

    If it was a rhombus it would be called one.

    But seriously of course it is a subset of the Rhombi (rhombuses) in the say way you would no problem saying it was a quadrilateral.

    So yes a square is a special type of rhombus in the same way it is a special type of quadrilateral.

    I dont use the word oblong I dont like it and rectangle does the job perfectly well so not getting drawn on that one!
  10. googolplex

    googolplex Occasional commenter

  11. Maths_Mike

    Maths_Mike New commenter

    My point being a square is not called a rhombus any more than you would call it a quadrilateral although it is a special example of both.

  12. tafkam

    tafkam Occasional commenter

    I do use the word oblong, but mainly to emphasise that rectangle doesn't just mean the oblong ones!
  13. The definitions are inclusive, so Quadrilateral includes rhombus, includes squares.

    I've never seen oblong on an exam paper and think it's always worth avoiding confusing children.
  14. tafkam

    tafkam Occasional commenter

    This is true, but I have seen children (and I'm not talking just a handful here) incorrectly think that a square is not a rectangle because they think only oblong rectangles count.
  15. i have seen children's edutainment programmes describing rectangles as having '2 long and 2 short' sides, which is why at ks2 i like to use the word 'oblong' to point up that 'rectangle' includes squares and oblongs - prisms are a good way of using 'rectangle' for the connecting faces as they can be oblongs or squares
    at ks1/ks2 qca cannot make its mind up on oblongs, and hasn't been able to do so for at least 10 years
    when focussing in on what exactly a shape is - yes, it's a parallelogram, but actually it' a rhombus - and you know what, it's a square - i use the analogy, you are a child, you are a girl, you are jane
  16. tafkam

    tafkam Occasional commenter

    ... and a rectangle... and a quadrilateral.
    It's good to realise that overlaps and subsets exist all over the place.
  17. i did draw up a chart of quadrilaterals once on the lines of the veenn diagram someone linked to - but easier to follow, i think - all roads lead to the square - lost it tho' drat it
    i do a 3d shapes sort with y4 or y5 (depending on when i get round to it) - spot the prism - always interesting to see who twigs that the cuboid and the cube.....
  18. A tomato is a fruit, a peanut is a legume and trapezium is a____________________________
    Fill in the blank please
    Serious questions [​IMG]

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