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- You Say Trapezium, I Say Trapezoid
- Exactly, Or at least?
- Implicitly Inclusive
- The Challenge of The Isosceles Trapezoid
We have to start with a regional issue: The word “trapezoid” doesn’t mean the same thing in every country. In our FAQ on geometrical formulas, we head one article with two names and a footnote: Taking the last issue first, when we get a question about a trapezium, we generally assume it is used in the European sense (though rarely we might see it i...
Now let’s move on to the other issue, which tends to generate more questions, like this one from 2004: I can’t vouch for the claim that most textbooks state the exclusive definition (saying that figures with a second pair of parallel sides are excluded from being trapezoids); but are they wrong, as this author reportedly says? Or is hewrong? I star...
On the other hand, it may be that they are really using the inclusive definition, but it isn’t obvious. Their wording may sound exclusive, but really beinclusive: We are so used to inclusive definitions that, in effect, we define “two” inclusively: If we say two sides are parallel, we are not mentioning the other sides, which may also be parallel! ...
Let me add one more comment: Under the inclusive definition, a parallelogram is a special kind of trapezoid. An often-unnoticed consequence is that we have to carefully define the other special kind of trapezoid, the isosceles trapezoid. This is commonly defined as a trapezoid in which the non-parallel sides are congruent. There are two problems he...
An isosceles trapezium is a trapezium in which the non-parallel sides are equal in measure. In other words, the bases are parallel and the legs are equal in measure. In this article, we will learn the properties of an isosceles trapezium.
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