Definition:Isosceles Trapezium

Definition

An isosceles trapezium is a trapezium whose legs are the same length.

Usage Differences

The North American definitions of trapezium and trapezoid differ from most of the rest of the world as follows:

a trapezoid has one pair of sides that are parallel

a trapezium does not have a pair of parallel sides.

This is the opposite way round from the definitions as used in most of the rest of the world, as used by $\mathsf{Pr} \infty \mathsf{fWiki}$.

In order to reduce confusion, when a trapezoid is intended, it may be better to use the term irregular quadrilateral instead of trapezoid.

It is worth noting that Euclid, in his definitions, did not distinguish between trapezia and trapezoids, and lumped them together as trapezia:

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 $22$)

Also see

• Results about isosceles trapezia can be found here.

Linguistic Notes

Isosceles

The word isosceles comes from the Greek: $\iota \sigma \omicron \sigma \kappa \epsilon \lambda \epsilon \varsigma$, that is: from iso meaning equal, and skelos meaning leg.

Thus an isosceles triangle is literally an equal-leg triangle.

It is pronounced eye-sos-ell-eez, that is, with the emphasis on the second syllable. Note that the c is silent.

The word skeleton comes from the same linguistic root.

Trapezium

The plural of trapezium is trapezia.

The word comes from Latin, in which language it is a neuter noun of the second declension, hence its plural form.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): isosceles trapezium
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): isosceles trapezium