Math CentralQuandaries & Queries


Question from Rachel:

Can a rhombus with all right angles still be tagged as a rhombus, or is it then said to be a square?

We have three responses for you

Hi Rachel,

A rhombus is quadrilateral with all side of equal length. Thus a quadrilateral with all sides of equal length and all angles right angles is still a rhombus but it is also a square. It is also a quadrilateral, a rectangle and a parallelogram.

Harley Weston


Hi Rachel.

A square is a special kind of rhombus, but it is still a rhombus.

Walter explains this pretty well with a diagram on this page in our archives.




In mathematics, experience has taught us that it is a good idea to use 'inclusive' definition.

So the definition of a rhombus (e.g. four equal sides, or two mirrors of symmetry through opposite vertices) includes squares within their scope. The properties are still there, so include the squares as (special) rhombi. (Also include a square as a special rectangle!)

If you think about any other property you identify for a rhombus (e.g. opposite sides parallel) these also hold for a square. In fact the reasoning used for these will also work for squares. It is not efficient to do the reasoning / remembering twice: once for rhombi, and again for the squares!

Also any formula you develop for rhombi will also apply to squares.

Walter Whiteley



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