Some girlfriend 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 interpretations of what those forms require.

You are watching: A square is a rectangle but a rectangle is not a square

Could who please provide a far better explanation or analogy so the I can show them the light.

Big pan of these kinds of funny facts/postulates/theorems. Please share if you deserve to think that others.



If you usage a colloquial meaning of rectangle - meaning "a four-sided form with four right angle that isn't a square" - then it can't it is in a square.

However, a more reasonable meaning of rectangle just way any four-sided shape with appropriate angles, which has squares.

Most rhombuses, however, are not rectangles. Just rhombuses that are also squares are likewise rectangles, due to the fact that a rectangle has 4 sides through equal angles, and also a rhombus has 4 equal sides.

I think you're misunderstanding the statement around a rhombus. Those friends were saying that squares are not rhombuses. That is, utilizing the same colloquial expertise as you cited because that the meaning of a rectangle: corresponding the definition, however not corresponding a much more specific an interpretation with its very own name.


They were utilizing a much more “colloquial” meaning in their understanding, rather of the much more “factorial tree” an interpretation of four sided shapes.

All apples room fruits. Not all fruits are apples.

To expand as to why we would certainly want to have squares being rectangles is to recognize the larger relationship.

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

A rectangle is a quadrilateral with four equal angles.

A rhombus is a square with four equal sides.

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

Squares room special instances of rectangles, rhombuses, and parallelograms.

Rectangles and also rhombuses space each special situations of parallelograms.

It is advantageous to have this hierarchy due to the fact that each more restrictive form inherits the properties of the much less restrictive shape. That is, a square "inherits" all of the properties and rules that govern rectangles, rhombuses, and parallelograms.

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

It's just extra work for no gain.

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level 2
Op · 3y

Hell yeah. Thanks.

level 1
· 3y

A square is ‘special’ situation of rectangle as it fits all the meanings of rectangle yet has one extra necessity to be a squares, like exactly how a red square is a square yet not squares space red squares

picture of rectangle

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


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Created Sep 5, 2008


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