It confused me the a parallel is never considered a rectangle, however a rectangle is considered a special case of a parallelogram.

How is this possible?


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I think you might be confused about necessity and sufficiency. E.g. Every Irishman is a mammal, offered that he meets the problems to be a mammal: live young, etc. Yet, no every mammal is an Irishman. Take the exciting wallaby as an example.

In the very same way, every rectangle is a parallel in the it satisfies the problems to be such a figure: the is a quadrilateral with two pairs of parallel edges. Yet, no every parallel is a rectangle. For, just like the Irishman, a rectangle has actually stricter conditions for member in that is set: the rectangle must furthermore have four right angles, and also the Irishman must be indigenous Ireland.

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This figure from Wiki might help. Think that $S$ as the class of rectangles and $N$ as the course of parallelograms. Or equivalently, Irishmen and mammals.


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Why is a rectangle a parallelogram, but a parallelogram is no a rectangle ?

Why room all cat animals, however not all animals are cats ?


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A rectangle is taken into consideration a special case of a parallel because:

A parallel is a quadrilateral v 2 bag of opposite, equal and also parallel sides.

You are watching: Can a parallelogram be a square

A rectangle is a quadrilateral through 2 pairs of opposite, equal and also parallel sides BUT ALSO creates right angles between nearby sides.


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It perplexed me that a parallel is never taken into consideration a rectangle, ...

This is just not true. Part parallelograms space rectangles, in certain the persons that have actually ninety level angles.


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Rect- , indigenous latin, method "right".Rectangle = That has actually right angles.And here you have actually a parallel without right angles:

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The same means that not all rectangles space squares, not all parallelograms are rectangles. A rectangle is a parallelogram through 4 best angles.


In a rectangle, that is imperative that each angle of the square is 90°. This is no true for every parallelograms because isn"t important that any kind of of the angle is 90°. All things have actually special cases. Through extension, you can say the a square is a special instance of both a rectangle and a parallelogram: The problem for a parallelogram is just for opposite sides to be same in length. You build this additional for a rectangle by do any and also therefore all angle to be 90. Finally, because that a square you impose the ALL the political parties be equal, making the a special instance of both! try to work out the relation between a rhombus and the others, that should give you some much more clarity.


Why is a mrs a person being, but a human being is not a woman?

You must recognize the exact meanings of the sentences about paralelograms and also rectangles:

The declare is the every rectangle is a paralelogram, similar to every woman is a human being being. That way that some paralelograms (women) space rectangles (humans), yet there deserve to exist other paralelograms (humans) which are not rectangles (women). The statement speak you nothing around them.

See more: Difference Between Greatest Common Factor And Least Common Multiple


A rectangle is a special instance of a parallel (ie a rectangle is a parallelogram through angles of 90º). A rectangle HAS to have actually angles of 90º, but a parallelogram does not.


From bigger sets of objects to smaller, more committed sets:

Quadrilaterals: close up door polygons v 4 sides

Parallelograms: Quadrilaterals through opposite political parties that are parallel

Rectangles: Parallelograms with right-angle corners

Squares: Rectangles with all political parties of equal length

A square is a rectangle, however a provided rectangle is no necessarily a square, etc. The squares space a subset of rectangles; the rectangles room a superset the squares. The same relationship holds for rectangles and also parallelograms.


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