How is this possible?

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

In the same way, every rectangle is a parallel in that it satisfies the problems to be together a figure: it is a quadrilateral with two bag of parallel edges. Yet, not every parallel is a rectangle. For, as with the Irishman, a rectangle has stricter problems for membership in the set: the rectangle must additionally have 4 right angles, and the Irishman have to be from Ireland.

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

*Why is a rectangle a parallelogram, yet a parallelogram is not a rectangle ?*

Why are all cats animals, but not all animals are cat ?

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

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

You are watching: Are all rectangles parallelograms true or false

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

It puzzled me that a parallel is never considered a rectangle, ...

This is simply not true. Some parallelograms room rectangles, in specific the persons that have actually ninety level angles.

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

The same means that not all rectangles space squares, no all parallelograms room rectangles. A rectangle is a parallelogram with 4 best angles.

In a rectangle, the is imperative the each angle of the quadrilateral is 90°. This is no true for every parallelograms because isn"t vital 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 case of both a rectangle and also a parallelogram: The condition for a parallel is just for opposite political parties to be equal in length. You build this additional for a rectangle by do any and also therefore all angles to it is in 90. Finally, because that a square you impose that ALL the sides be equal, making the a special instance of both! try to job-related out the relation between a rhombus and the others, that should give you some more clarity.

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

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

The declare is the every rectangle is a paralelogram, as with every mrs is a human being being. That means that some paralelograms (women) room rectangles (humans), yet there have the right to exist various other paralelograms (humans) which room not rectangles (women). The statement speak you nothing about them.

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

From bigger sets the objects come smaller, more committed sets:

Quadrilaterals: closed polygons v 4 sides

Parallelograms: Quadrilaterals through opposite sides that space *parallel*

Rectangles: Parallelograms through *right-angle* corners

Squares: Rectangles through all political parties of equal length

A *square* is a *rectangle*, yet a given *rectangle* is no necessarily a *square*, etc. The squares are a subset the rectangles; the rectangles are a superset of squares. The same connection holds for rectangles and parallelograms.

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

Is a parallelogram v equal sides necessarily a rhombus? Is one through 4 appropriate angles (or congruent diagonals) have to a rectangle?

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