It perplexed me the a parallel is never taken into consideration a rectangle, however a rectangle is taken into consideration a special situation of a parallelogram.

How is this possible?


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I think you might be confused around necessity and sufficiency. E.g. Every Irishman is a mammal, offered that the meets the conditions to be a mammal: live young, etc. Yet, not every mammal is an Irishman. Take the delightful wallaby as an example.

In the exact same way, every rectangle is a parallel in the it satisfies the conditions to be together a figure: it is a quadrilateral through two bag of parallel edges. Yet, not every parallel is a rectangle. For, just like the Irishman, a rectangle has actually stricter conditions for member in the set: the rectangle must in addition have four right angles, and also the Irishman need to be from Ireland.

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This number from Wiki might help. Think of $S$ together the course of rectangles and also $N$ together the class of parallelograms. Or equivalently, Irishmen and mammals.


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

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


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A rectangle is considered a special case of a parallel because:

A parallel is a quadrilateral through 2 pairs of opposite, equal and also parallel sides.

You are watching: Why is a quadrilateral only sometimes a parallelogram?

A rectangle is a quadrilateral v 2 bag of opposite, equal and parallel sides BUT ALSO forms right angle between surrounding sides.


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

This is merely not true. Some parallelograms are rectangles, in certain the persons that have actually ninety level angles.


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Rect- , native latin, way "right".Rectangle = That has actually right angles.And below you have a parallel without best angles:

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The same means that no all rectangles space squares, no all parallelograms space rectangles. A rectangle is a parallelogram v 4 right angles.


In a rectangle, that is imperative that each edge of the quadrilateral is 90°. This is not true for every parallelograms due to the fact that isn"t crucial that any of the angles is 90°. Every things have actually special cases. Through extension, you deserve to say the a square is a special instance of both a rectangle and a parallelogram: The condition for a parallelogram is only for opposite sides to be same in length. You build this additional for a rectangle by making any and also therefore all angle to be 90. Finally, for a square girlfriend impose the ALL the political parties be equal, making it a special case of both! try to work out the relation between a rhombus and also the others, that should offer you some an ext clarity.


Why is a woman a human being being, yet a human being is not a woman?

You must understand the exact meanings of the sentences around paralelograms and also rectangles:

The explain is that every rectangle is a paralelogram, just like every woman is a person being. That way that part paralelograms (women) room rectangles (humans), yet there can exist other paralelograms (humans) which space not rectangles (women). The statement tells you nothing around them.

See more: How Many Ml In An Insulin Syringe, Is 1 Ml 100 Units On An Insulin Syringe


A rectangle is a special situation of a parallelogram (ie a rectangle is a parallelogram through angles the 90º). A rectangle HAS to have actually angles the 90º, however a parallelogram does not.


From bigger sets of objects come smaller, more specialized sets:

Quadrilaterals: closeup of the door polygons through 4 sides

Parallelograms: Quadrilaterals through opposite sides that space parallel

Rectangles: Parallelograms v right-angle corners

Squares: Rectangles v all sides of equal length

A square is a rectangle, but a provided rectangle is not necessarily a square, etc. The squares space a subset that rectangles; the rectangles are a superset that squares. The same connection holds for rectangles and parallelograms.


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