When is a trapezium not a trapezium?

Why, when it's a trapezoid of course.

There are some days when the English language is soooooo frustrating. What version should I use? Standard Australian English (SAE)? American English? British English? Living as I do in a land of many expats, from various corners of the world, I've had to learn some extra words and meanings.

Earlier this week a colleague commented to me about this topic and then e-mailed me some further information about it. The problem arose when he was teaching his students about 2-D shapes, using his personal knowledge of 50+ years, to teach them the names of various quadrilaterals. Now this learned gentleman comes from the USA, so he naturally used the US terminology, just as I would naturally use the Australian terminology. Not a problem you might say. Well, for most shapes, you are correct. There is no problem because there is no difference in the shape names. A triangle is a triangle, a square is still a square, a rectangle is definitely a rectangle (although a few might also call it an oblong), a parallelogram is still a parallelogram (or maybe it's a rhomboid), a rhombus is still a rhombus, and a kite is still a kite, no matter which side of the ocean you might be on.

But what do you call a quadrilateral with exactly one pair of parallel sides? That's where the problem comes in. If you are from the USA, then you will call it a trapezoid, but if you're an Aussie (or using an Aussie mathematics curriculum), then it is a trapezium! OK, that doesn't seem like a big issue. The problem comes in when you discover that the folk from the USA consider a trapezium to be a quadrilateral with no parallel sides. We Aussies would just call that an irregular quadrilateral!

So, I just did a search trying to find out how this anomaly came about, and found this interesting article. It seems like this problem has been around since 1795, and a resolution has yet to be determined. For those of you who like pictures, here's one I found, this one summarises the quadrilateral family quite neatly.

Oh the joys of the English language! I guess it's yet another situation where we have to think carefully about our audience, and then say, "it's not wrong, it's just different", unless you're preparing students for an exam which specifically uses one definition or the other, in which case you'd better make sure you know which one is considered correct by the examiners.

So what are we teaching our students? In the interests of consistency across the grades from K to 5, we'll call it a trapezium, but it the kids ask the question, then I'm happy to say that I will now be able to enlighten them, thanks to my learned colleague from the USA, and some Internet research.