How is this possible?

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.

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.

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

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

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.

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.

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

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.

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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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How huge does a rectangle have to be so the while rotating it, another smaller rectangle behind the is never ever visible?

Is a parallelogram through equal political parties necessarily a rhombus? Is one through 4 best angles (or congruent diagonals) have to a rectangle?

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