# Why is a trapezoid a quadrilateral, but a quadrilateral is not always a trapezoid?

When you consider the relationship between two shapes, it is useful to do so from both standpoints, i.e. *necessary* vs. *sufficient*.

Necessary -

Sufficient - The qualities of

Questions you might want to ask:

- Can a trapezoid exist without possessing the qualities of a quadrilateral?
- Are the qualities of a quadrilateral sufficient to describe a trapezoid?
Well, from these questions we have:

- No. A trapezoid is defined as a quadrilateral with two parallel sides. Therefore, the quality of "quadrilateral" is necessary, and this condition is satisfied.
- No. Any other shape can have four sides, but if it does not have (at least) two parallel sides, it
*cannot*be a trapezoid. An easy counterexample is a boomerang, which has*exactly*four sides, but*none of them are parallel*. Therefore, the qualities of a quadrilateral do not sufficiently describe a trapezoid and this condition is not satisfied.Some crazy examples of quadrilaterals:

This means that a trapezoid is too specific of a quadrilateral that merely having the quality of "quadrilateral" does not guarantee the quality of "trapezoid".

*Overall, a trapezoid is a quadilateral, but a quadrilateral doesn't have to be a trapezoid.*

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*Answer from HIX Tutor*

*When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.*

*When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.*

*When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.*

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