# 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.

6. ### adamcreenOccasional 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. ### 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

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!

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____________________________
Fill in the blank please
Serious questions