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

##### 1 Answer

Nov 12, 2015

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.*