Definition:Quadrilateral/Trapezoid

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Definition

A trapezoid is a quadrilateral which has exactly one pair of sides parallel:

Trapezoids.png


Thus, by this definition, a parallelogram is not a trapezoid.


Base

The bases of a trapezoid are its $2$ parallel sides.

In the above diagram, the bases of the given trapezoids are $AB$ and $DC$, $EF$ and $HG$, and $IJ$ and $KL$.


Leg

The legs of a trapezoid are its $2$ sides adjacent to the bases.

In the above diagram, the legs of the given trapezoids are $AD$ and $BC$, $EH$ and $FG$, and $IK$ and $JL$.


Height

The height of a trapezoid is defined as the length of a line perpendicular to the bases.

In the above diagram, the heights of the given trapezoids are indicated by the letter $h$.


Also defined as

Outside the US (one of a few countries that use this definition), a trapezoid is a quadrilateral with no parallel sides, that is, what the US defines as a trapezium.


Also known as

Outside the US (one of a few countries that use this definition), this figure is known as a trapezium.


Euclid, in his definitions, did not distinguish between trapezia and trapezoids.


Also see

  • Results about trapezoids can be found here.


Euclid's Definitions

In the words of Euclid:

Of quadrilateral figures, a square is that which is both equilateral and right-angled; an oblong that which is right-angled but not equilateral; a rhombus that which is equilateral but not right-angled; and a rhomboid that which has its opposite sides equal to one another but is neither equilateral nor right-angled. And let quadrilaterals other than these be called trapezia.

(The Elements: Book $\text{I}$: Definition $22$)