Is a square a rhombus?

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

1. lynnestartin

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?

4. DMNew commenter

Oops double post (only one with correct spelling)!

5. stuartwithau

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.

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. tafkamOccasional 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!

9. Maths_MikeNew commenter

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!

QED

12. Maths_MikeNew 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.

13. tafkamOccasional commenter

I do use the word oblong, but mainly to emphasise that rectangle doesn't just mean the oblong ones!

14. siddons_sara

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.

15. tafkamOccasional 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.

16. florapost

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

17. tafkamOccasional commenter

... and a rectangle... and a quadrilateral.
It's good to realise that overlaps and subsets exist all over the place.

18. florapost

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.....

19. Betamale

A tomato is a fruit, a peanut is a legume and trapezium is a____________________________