Some friends of mine were trying to argue that a square is not and can not be a rectangle (or a rhombus, etc.) based on their half-baked meanings of what those forms require.

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Could who please carry out a better explanation or analogy so that I might show lock the light.

Big fan of these type of fun facts/postulates/theorems. Please share if you can think that others.



If you use a colloquial an interpretation of rectangle - definition "a four-sided shape with four right angle that isn't a square" - climate it can't be a square.

However, a more reasonable meaning of rectangle just method any four-sided form with right angles, which has squares.

Most rhombuses, however, are not rectangles. Just rhombuses the are likewise squares are likewise rectangles, since a rectangle has four sides with equal angles, and a rhombus has four equal sides.

I think you're misunderstanding the statement about a rhombus. Those friends were saying that squares space not rhombuses. That is, utilizing the exact same colloquial understanding as you cited for the definition of a rectangle: matching the definition, but not equivalent a an ext specific meaning with its very own name.


They were making use of a much more “colloquial” definition in their understanding, instead of the more “factorial tree” meaning of four sided shapes.

All apples are fruits. Not all fruits space apples.

To expand as to why we would want to have actually squares gift rectangles is to understand the larger relationship.

A square is a quadrilateral with 4 equal sides and also four equal angles.

A rectangle is a quadrilateral with four equal angles.

A rhombus is a quadrilateral with four equal sides.

A parallel is a quadrilateral whereby both pairs of opposite sides are parallel.

Squares are special cases of rectangles, rhombuses, and also parallelograms.

Rectangles and also rhombuses are each special situations of parallelograms.

It is useful to have actually this hierarchy since each more restrictive shape inherits the properties of the less restrictive shape. The is, a square "inherits" all of the properties and rules that govern rectangles, rhombuses, and also parallelograms.

If friend exclude squares from being rectangles, because that example, then any property the holds because that a rectangle girlfriend now have actually to clearly state it likewise holds for squares.

It's simply extra job-related for no gain.

See more: What Does Its On A Contract Mean On A Contract'S Signature Line?

level 2
Op · 2y

Hell yeah. Thanks.

level 1
· 2y

A square is ‘special’ case of rectangle together it fits all the definitions of rectangle however has an extra need to be a squares, like just how a red square is a square but not squares are red squares

picture the rectangle

So this is a rectangle and also square is a rectangle whereby x=y

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Created Sep 5, 2008


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