Talk:Trapezoid/Archive 1

Miscellaneous comments
Parallelogram should only be considered as a degenerate form of a trapezoid. There is large class of problems which deal with similar triangles which effectively treat trapezoid as that which remains once a similar triangle (with a parallel side) is removed from a larger triangle. These do not make any sense for a parallelogram. A parallelogram is no more a proper trapezoid than a circle is a proper ellipse. — Preceding unsigned comment added by Drubanov (talk • contribs) 08:09, 7 March 2015 (UTC)
 * But a circle is an ellipse, with zero eccentricity and equal major and minor axes, just as a square is a special case of a rectangle and a parallelogram. I agree that there are a few problems where one needs to specify a trapezoid that is not a parallelogram, but there is an even larger class of problems where it is essential to use the inclusive definition.    D b f i r s   12:12, 7 March 2015 (UTC)

Perhaps you should have references here. Isn't the rule, No reference. No article? If some don't show up, someone will prod it for deletion! —Preceding unsigned comment added by 69.246.54.228 (talk) 01:53, 19 September 2007 (UTC)

There are thousands of possible references: almost any school text book, or any dictionary will suffice.  D b f i r s   07:10, 10 September 2012 (UTC)

Note that a trapezium (British English) or trapezoid (American English) does not have two parallel sides. What kind of beast is a (U.S.)trapezium ? --FvdP 19:37, 12 Mar 2004 (UTC)


 * A USA Trapezium is what the rest of the world calls trapezoid (no sides parallel). For whatever reason the Americans swapped the name. &mdash; Jor (Talk) 19:20, 1 Apr 2004 (UTC)


 * The matter is utterly confusing. At the top of the page a trapezoid has two parallel sides. At the bottom said four sided figure has no tow sides parallel. Querobert August 21 2004


 * Is it just me, or does the second paragraph on the front page have the two terms swapped? We seem to have agreed on the following:
 * A quadrilateral with one pair of parallel sides is called a trapezoid in the US, and a trapezium in the UK;
 * A quadrilateral with no pair of parallel sides is called a trapezium in the US and a trapezoid in the UK.
 * However, the second paragraph of the article as it stands seems to directly contradict the second line above. Am I mistaken, or is it? After all, comments asserting the correctness of a paragraph can never themselves be wrong... Pmdboi 21:21, 17 January 2007 (UTC)
 * I went ahead and corrected it. Pmdboi 17:27, 18 January 2007 (UTC)
 * You are of course correct. A bad edit was made a week ago by an anon, who of course did not bother to satisfy my request for prior discussion. -- Meni Rosenfeld (talk) 17:20, 21 January 2007 (UTC)
 * Problem seems to have returned. The first and second paragraphs contradict each other on term/location. Wuzzled 11 September 2007 —Preceding unsigned comment added by Wuzzled (talk • contribs) 22:24, 11 September 2007 (UTC)
 * It is okay. Try reading the second paragraph again. -- Meni Rosenfeld (talk) 22:49, 11 September 2007 (UTC)

In the United States, a trapezoid has two parallel sides. &mdash; 131.230.133.185 10:30, 3 August 2005 (UTC)
 * (Edit by Arbiter) I'm changing the terms back to the way they're supposed to be according to every real dictionary... trapezoid is a British construction, trapezium is the American one (despite what you've heard in school). —Preceding unsigned comment added by 66.182.140.100 (talk) 15:44, 24 March 2008 (UTC)
 * 66, your edit contradicts the dictionary reference at the bottom of the page. Do you have a reference supporting your edit?  --Allen (talk) 16:05, 24 March 2008 (UTC)
 * In fact trapezoid is seldom used in the UK, and when it is used, it normally coincides with the American sense. '' d b f i r s   22:46, 24 March 2008 (UTC)


 * I've reverted the edits by 66.182.140.100 who must be reading a confused dictionary. The word trapezoid almost exclusively and almost ubiquitously denotes a shape with two parallel sides, even in the UK where trapezium is more commonly used with this meaning for the quadrilateral.  Both terms have been used in the past for a shape with no parallel sides, but it is a hundred years since this usage was common in the UK.  Nearly all UK schools simply speak of an irregular quadrilateral, and have no special term corresponding to the American trapezium.  The usage is confusing however you explain it!  ''  d b f i r s   23:00, 24 March 2008 (UTC)

In the beginning of the article it says: "a four-sided figure with one pair of parallel sides is referred to as trapezoid in American English" but then on the Definition and terminology section it says "In North America, the term trapezium is used to refer to a quadrilateral with one pair of parallel sides.". The second statement contradicts the first one in my opinion. Am I missing something? After some reading (the article, the discussion page and the Oxford Dictionary) I understand that the second statement should say "In North America, the term trapezoid is used to refer to a quadrilateral…". I would have done the change myself but since the topic looks super confusing and I've never edited the wiki before I didn't dear to. --Carles Tomás Martí (talk) 08:04, 21 October 2009 (UTC)
 * Yes, thank you for pointing this out. We missed the fact than anon editor 82.39.201.139 vandalised the article (possibly accidentally through lack of understanding) a fortnight ago.  I've restored the correct wording.  The usage certainly is confusing, it took me ages to discover the complex history of the two words.  We could make life much simpler if we could remove dated definitions from dictionaries, but they are legitimately there, because the words were once used with other meanings.    D b f i r s   21:33, 21 October 2009 (UTC)
 * I propose that we demote the confusing history and dated definitions to a note at the end, and simply state in the introduction that the article is about the American trapezoid and the British trapezium. What does anyone else think?   D b f i r s   21:37, 21 October 2009 (UTC)

"A quadrilateral that has exactly two sides parallel.", see f.e. http://www.math.com/school/glossary/defs/trapezoid.html.

I hate the definition because 1) I used to think a parallelogram is a trapezoid and 2) I know about open sets and closed sets and I beleve a practical definition should define a closed set, not an open one.

So my question to contributors: did you mean "exactly two sides parallel" or "at least two sides parallel"? and what should we do with all that? --GS 14:34, 18 Apr 2005 (UTC)

Indeed, in grade school (at least in Ontario, Canada), students are being taught that a trapezoid must have exactly two parallel sides; i.e., a parallelogram is not a trapezoid. This is inconsistent with other definitions that I have seen, so there certainly seems to be some controversy over the matter. In fact, the exactly-two-parallel-side definition seems to be the most prevalent, so this Wikipedia article should probably be updated to at least mention this definition. -Pomakis 17:18, 29 January 2006 (UTC)


 * (in reply to your recent edits to the above) I suggest that you take this matter up with math.com and your grade school. Most mathematicians prefer the inclusive definition, so this is the one that is (mainly) used in the article.  I agree that the confusion is annoying.  As Meni points out (below), the article does mention the restrictive (exclusive) definition that you were taught.  Some schoolteachers like the restrictive definition because it allows only one answer to the question "what is this shape called?"  (Other teachers prefer to ask more precise questions.)   D b f i r s   07:24, 10 September 2012 (UTC)

It means "at least" two sides parallel, to fit in the diagram which includes all quadrilaterals. "all Parallelograms are Trapeziums, all Trapeziums are Quadrilaterals" "some Quadrilaterals are Squares, all Squares are Parallelograms, which in turn, makes them Trapeziums" --Rkeysone 14 September 2006

The definition sounds a little mushy because it includes the following two contradictory lines:

"Some authors define it as a quadrilateral having exactly one set of parallel sides, so as to exclude parallelograms." "If the other set of opposite sides is also parallel, then the trapezoid is also a parallelogram" Seems some editing is it order. —Preceding unsigned comment added by 68.77.148.122 (talk) 12:40, 5 September 2007 (UTC)
 * "Some authors", not "all authors". You have also missed the line "[This article] admits parallelograms as special cases...". -- Meni Rosenfeld (talk) 12:48, 5 September 2007 (UTC)

Area
How come the area is (L1+L2)/2×H
 * Split the T. to two triangles, calculate and sum. What is your answer, anyway? --GS 14:18, 26 Apr 2005 (UTC)

Absolutely Merge it
goldenrowley 8-6-06

Different types of trapazoids
Requested: add different type of trapazoids. ex: isosceles trapazoid
 * Well, isoceles trapezoid is already discussed, what others do you have in mind? In either case, be bold! -- Meni Rosenfeld (talk) 16:30, 13 December 2006 (UTC)
 * Right trapezoid — Ti89TProgrammer 04:14, 10 October 2007 (UTC)

Definition of 'Midsegment'
Requested: please account for the definition of a midsegment in the case of parallelograms. The currently used definition of a trapezoid (i.e. a shape with two parallel sides) allows for the inclusion of parallelogram, which is fine. However, the definition of a midsegment then states that the midsegment is to be drawn from the midpoints of the non-parallel sides, which a parallelogram does not have. So, either a parallelogram doesn't have a midsegment (this, I think, is not the correct solution) or the definition of a trapezoid needs to be more restrictive to not include parallelograms (not everyone would be happy with that) or, and this is likely the best solution, the definition of a midsegment of a trapezoid needs to be modified to account for the case of parallelograms.
 * I've made a modification which aspires to solve this issue. -- Meni Rosenfeld (talk) 16:30, 13 December 2006 (UTC)

Circumscribed trapezoids / quadrilaterals
Maybe we should add some information about this too? --HappyCamper 19:59, 10 March 2007 (UTC)

Is parallelogram a trapezium(or trapeziod)?
Yes, I agree with the taxonomic classification of quadrilaterals illustrated. Parallelogram is just a special case of trapezium(or trapeziod). Let's consider the formulae used for parallelogram and trapezium(or trapeziod) in producing their area. The relationship in between them(the formulaes) agrees with the taxonomic classification of quadrilaterals illustrated. Thus, hereby i conclude that, PRACTICALLY, parallelogram is just a special case of trapezium(or trapeziod); it is a trapezium (or trapeziod).


 * by Sia S.H. 7th of April, 2007

I disagree with the classification above. There are no useful inherited properties in defining a parallelogram as a special case of trapezoids. The most notable disadvantage, however, is that there is now no word reserved for referring to a quadrilateral with exactly one pair of parallel sides. You cannot call it a "trapezoid" because some schmuck might say "well, technically, that could still be a parallelogram." Every textbook I have ever seen defines a trapezoid as a category exclusive of parallelograms. —Preceding unsigned comment added by Cyclehausen (talk • contribs)


 * That's like defining rectangles to exclude squares, or defining continuous functions to exclude differentiable functions. Such an approach is rare in mathematics, and its reasons for being commonly adopted in the case of trapezoids are traditional, not mathematical. -- Meni Rosenfeld (talk) 15:49, 30 June 2007 (UTC)

It really is not the same. When you talk about continuous functions, you are referring to a set of properties that they have that are useful. Differentiable functions inherit all of these useful properties (most notably the value of the two-sided limit at equalling the value of the function every point on the interval), and add a set of their own.

Squares inherit a number of useful properties from rectangles, and admitting squares as a special case of rectangles (and rhombi) allow them to inherit all the useful properties from each superset.

There ARE NO useful properties of trapezoids. They simply are (I attest) quadrilaterals with exactly one set of parallel sides. The only property that comes from this that MIGHT be considered a useful inheritance for parallelograms is the area formula, if you choose to see the parallelogram's area formula as a degeerate case of the trapezoid formula. And how useful is that, really? Yes, there is also the fact that the diagonals cut each other in the same ratio, but in a parallelogram the much more useful property that the diagonals bisect each other exists. Even the 4-side area formula for trapezoids fails to be valid when the shape is a parallelogram. The primary reason in all practical practice, both formally mathematical and secular, to use the term "trapezoid" is to DIFFERENTIATE it from a parallelogram.

Plese remain mindful that in Geometry, definitions have their greatest value when we use them to prove things. No proof of which I am aware for parallelograms utilizes any inherited properties of trapezoids that cannot be easily established from the definition of the parallelogram "A quadrilateral with two pairs of parallel sides" instead. That may seem obvious, and that is exactly why classifying a parallelogram as a trapezoid is unnecessary and confusing.

I do appreciate the counter-argument, but I must ask for some North-American textbook references that support it. Perhaps the American and British traditions of trapezoid warrant completely separate pages. Cyclehausen 11:04, 1 July 2007 (UTC)
 * I do not argue with exclusion of parallelograms being more common in the literature (though I have no references one way or the other). Consequentially, I have no objection to excluding parallelograms in the article, as Wikipedia is, after all, an encyclopedia. Regardless, though the points you make may be valid, I am not convinced that mathematically speaking, excluding parallelograms is superior. -- Meni Rosenfeld (talk) 11:31, 1 July 2007 (UTC)
 * There is one notable advantage you gain if you exclude parallelograms: a "pure trapezoid" is determined by the lengths of its sides. This is obviously not true for parallelograms. This is probably the reason why some people restrict the definition. I think that this fact should be mentioned on the page.  —Preceding unsigned comment added by 147.175.96.224 (talk) 08:44, 30 April 2008 (UTC)
 * The glitch in the formula is mentioned at the appropriate point after the formula for area using just sides. Does anyone use this formula?    D b f i r s   09:44, 1 May 2008 (UTC)

I really would be happy with a separate paragraph being devoted to the option to include or exculde, rather than a simple aside in the opening paragraph about it. I think the dichotomy is certainly notable. My main problem is that in Mu Alpha Theta (the high school mathematics competitive honor society) the definition I present is used and standardized, as it is in every high schoolt ext I have ever encountered, and students tend to try to dispute questions that implement our standard by referring to this article. It gets old.Cyclehausen 11:47, 1 July 2007 (UTC)
 * I suppose this can be a good change, but I am not currently inclined to do it myself. I will be more than happy to help if you decide to try this yourself. -- Meni Rosenfeld (talk) 16:42, 1 July 2007 (UTC)

A "pair of parallels" or a "set of parallels"?
Someone in hope to improve clarity changed "pair of parallels" sides of the trapezoid to "set of parallels" sides. I am not sure what "set" means in the geometry context. Isn't "pair" clear? Ricardo sandoval 03:28, 24 August 2007 (UTC)
 * Pair seems quite clear to me, and definitely better than "set". Pair is more specific, since a pair is a set with two elements.  Doctormatt 18:34, 24 August 2007 (UTC)

"Exactly opposite"
The article now correctly gives the two terms for what North Americans call a trapezoid, but then says:
 * The exactly opposite concept, a quadrilateral that has no parallel sides, is referred to as a trapezium in North America, and as a trapezoid in Britain and elsewhere.

There is no "exactly opposite concept" to that of a quadrilateral that has parallel sides. The intended meaning is that the assignment of words to concepts is exactly opposite.

I suggest the phrasing:
 * Unfortunately, the same two terms are also used to refer to a quadrilateral with no parallel sides, in exactly the opposite manner: this is called a trapezium in North America and a trapezoid in Britain and elsewhere.

The article continues:
 * To avoid confusion, this article uses the North American wording.

This seems to imply that the North American wording, or rather terminology, is less confusing. The intended meaning must be that, to avoid confusion, the article uses only one convention, and it happens to be the North American one.

I suggest simply saying:
 * This article uses the North American term.

Normally I would just make these edits, but there is a warning saying not to touch this paragraph without first discussing it over here, so here I am.

--207.176.159.90 10:21, 1 September 2007 (UTC)


 * It's great that you have followed the request in the comment. In fact, it was placed there because of numerous people who were not aware of the alternative term, haven't bothered to actually read the paragraph, but only "knew" that trapezoid is NA and trapezium in UK, so they have switched the terms in the paragraph. Ironically, such people have continued to do so even after the comment was placed. Changes of phrasing are still welcome in the spirit of WP:BOLD.
 * As for the changes you suggest - I would say that, if it is understood that the object of our discussion is quadrilaterals, then "a quadrilateral with a pair of parallel sides" is the opposite of "a quadrilateral with no pair of parallel sides". I have added such a clarification, which I prefer to your suggestion since it emphasizes the contrast between the terms.
 * I would also say that the alleged implication of "to avoid confusion" is a bit of a strecth, but I see no harm in dropping that part, as you propose.
 * I have changed the article accordingly, see if it looks better to you. -- Meni Rosenfeld (talk) 12:42, 1 September 2007 (UTC)


 * I agree with 207; a quadrilateral with two parallel sides is not the "opposite" of one with no parallel side, and they certainly are not exactly opposite. It is the wording that is opposite.  Meni, do you have a source that the two shapes themselves are considered "opposites" of each other?  --Allen (talk) 16:01, 24 March 2008 (UTC)


 * I have made changes similar to what the original poster suggested. I also took out the giant "do not change without discussion" warnings on the sentence, which seem unnecessary to me.  I also added "according to Merriam-Webster" to clarify why we're making this claim about the terms.  I suspect the reason we've had trouble with people changing this is that Dbfirs is right when they imply above that the dictionary is wrong.  (Dbfirs says, "The word trapezoid almost exclusively and almost ubiquitously denotes a shape with two parallel sides, even in the UK...")  But as Dbfirs also seems to imply by upholding the current claim in the article, we have little choice but to go with our one so-called reliable source.  --Allen (talk) 02:31, 27 March 2008 (UTC)
 * Oh yeah, and if we get a bunch of people switching the wording despite the changes I've made, I won't oppose putting the "do not change" note back in. --Allen (talk) 02:33, 27 March 2008 (UTC)
 * To be fair to Merriam-Webster, they were probably correct when the dictionary was compiled (100 years ago?), but I have collected a set of citations to prove my assertion that their claim (and that of other US websites) about British usage is no longer true. I did find one Wikipedian who was taught the old usage at school (by an old Maths teacher) so I can't claim that the alleged British meaning is totally obsolete, just that it is very rare in modern usage.  The problem is that both words originally meant just a more general quadrilateral than a parallelogram.  Distinguishing shapes with one pair of parallel sides is a distinction not considered by Euclid, and attempts to make the distinction have been confused (blame Proclus?).  Perhaps the best place for my citations would be on this discussion page, rather than cluttering up the article?  What does anyone else think?  ''  d b f i r s   08:00, 27 March 2008 (UTC)

What about the other one?
In the last comment, I suggested "uses the North American term" because, after the discussion about the two versions of the terminology, the article turns out to be about trapezoids(NA) only. That's fine if that's what you're interested in, but what if you wanted to read about trapezoids(UK)? Looking under trapezium doesn't help: it's just a redirect to trapezoid. There seems to be no article about the trapezoid(UK), and I don't see why there shouldn't be one.

However, there isn't much to say about it, other than repeating the same content about the two conflicting usages. So what I suggest is that the two figures be treated as a single subject: although the usual rule in Wikipedia is one article per subject, I think it would make sense for this to be an exception.

So I propose that this article be renamed to something like "The trapezium and the trapezoid". Describe the two usages. Discuss the etymology (trapezium(UK) from the same root as "trapeze", as per its parallel sides; "-oid" because the pair of parallel sides wasn't there) and how the reversal of senses happened (one influential book, the OED says). The sort of thing that the article on long and short scales does. Then finally say "The rest of this article uses the North American terminology" and go on to discuss the trapezoid(NA) as now, and then briefly and the trapezium(NA). Howzat?

--207.176.159.90 10:34, 1 September 2007 (UTC)


 * That is, indeed, an interesting conundrum. I think the solution is: There is really nothing to be said about trapezium (NA), hence it is not notable enough to deserve an article. The article Trapezoid should use the NA wording, and mention trapezia (is that the correct plural?) only by virtue of their connection with trapezoids. In this context, mentioning the NA/UK confusion is appropriate, and explanations of etymology (about which I personally know nothing) would also be desirable. -- Meni Rosenfeld (talk) 12:53, 1 September 2007 (UTC)

"UK and elsewhere"
It's a little vague to lump everything together. Australians officially use trapezium for a quadrilateral with one set of parallel sides (as in UK), but also use trapezoid informally (as in NA) because of the influence of American educational shows. The quadrilateral with no parallel sides never had a special name - we always simply called it an irregular quadrilateral. Aspirex 10:23, 4 December 2007 (UTC)
 * We certainly cannot make any guarantees about how every person on earth chooses to call this. I think as long as a significant majority of non-American countries officially use the British convention (which is consistent with your statement), the claim in question is valid. -- Meni Rosenfeld (talk) 12:03, 4 December 2007 (UTC)
 * American "math" reference websites seem to believe that British people commonly use the word trapezoid to mean an irregular quadrilateral. This may have been the case a hundred years ago, but the word is rarely used in the UK now, and modern usage usually denotes either a British trapezium (= US trapezoid), or a 3-D shape having faces with some parallel sides.  The statements in the article and on American websites are misleading about modern usage.  ''  d b f i r s   10:41, 24 March 2008 (UTC)
 * Merriam-Webster gives a definition of a usage which was dying out in Britain a hundred years ago when this dictionary was printed (1913?) and is now virtually obsolete. Mathworld uses this out-of-date American view of British usage.  In modern usage, trapezoid means the same almost everywhere, thus the article title is valid, and needs only the caveat that the article describes what is more usually called a trapezium in Britain and elsewhere.  Perhaps it would be better to relegate the confusing American definition of trapezium to a footnote?  In fact, both terms have been used, from Euclid onwards, to describe any general quadrilateral (more general than a parallelogram).  The confusion arose from an ambiguous statement by Proclus.

The following show that modern non-American usage of the word trapezoid coincides with American usage.


 * This is nonsense and you are an idiot. Merriam-Webster is unused in the UK (thank goodness) and the ignorance (oh so typically American) of your assumption that adverts by a smattering of American companies is in any way an indicator of British nomenclature is laughable. Unsigned comment added by anon:82.8.131.151, a "Virgin Media" address possibly located in London, England.


 * I think the ignorance and assumptions are on your part. I am more British than you are, I don't use Merriam-Webster, and I carefully chose British adverts and usages.  Have you read the discussion?    D b f i r s   11:13, 6 January 2011 (UTC)


 * Most of these citations are invalid. There is a difference in the UK between noun-usage (Trapezium) and adjectival usage (Trapezoid or less commonly Trapezoidal). In the same way that no one would say "Hexagon table" (correct usage is "Hexagonal"), neither would anyone say "Trapezium table". —Preceding unsigned comment added by 88.105.28.221 (talk) 09:17, 18 April 2008 (UTC)
 * Fair comment, but the adjectival use derives from the noun definition, and thus serves to illustrate current usage.
 * -- or are you claiming that trapezoid is now just the adjective from the noun trapezium? If so, then my case is proven!  Dbfirs (talk) 07:18, 21 April 2008 (UTC)
 * Trapezoid is derived from the noun Trapezium. It is defined as an object that has the shape and properties of a trapezium - a desciptive, making it an adjective useage. As usual, American English has taken liberties with the original version and created yet another way to confuse people. (btw. the old spelling was TrapeSium, but that seems to have been replaced by the z-ists). 0300 02-06-10
 * I agree that the word "trapezoid" is more often used adjectivally outside the USA. It was Charles Hutton who caused confusion by mis-reading a translation of Proclus on the difference between trapezium and trapezoid, but both words are now used for the shape with one pair of parallel sides.  The spelling was never with an "s" (but you knew that, didn't you?).    D b f i r s   06:49, 2 June 2010 (UTC)


 * Could we just have a UK wiki??????? (solve so many problems! Cos it 'ain't color it's colour! :-D ) from a nosey moose --81.178.196.9 (talk) 11:21, 22 December 2010 (UTC)


 * Well most of us cope with regional variations in spelling. What is more confusing is the differences in the meaning of words, but once you are aware of the difference, it is not a serious problem.    D b f i r s   11:28, 6 January 2011 (UTC)

Contradictory statement
The sentence which begins "The exactly opposite kind of quadrilateral ..." obviously contradicts the previous paragraph. Along with other editors, I have not corrected it because of the request to discuss it here first, but it has long needed correction. I hereby give notice that I intend to correct this statement, (also removing the claim that the word trapezoid is regularly used in the UK). The whole area is a minefield because of contradictory usage, so I shall edeavour to retain a neutral point of view, retaining the US usage since that was the original article. Is this OK?  d b f i r s   10:07, 17 January 2008 (UTC)
 * this is the correct version. I don't know if you were referring to this or the wrong version. Note that countless hours of work have been dedicated to making sure this paragraph is correct, and except for brief periods of time after some smart-ass tries to change it, it is perfectly valid. -- Meni Rosenfeld (talk) 11:30, 17 January 2008 (UTC)
 * By the way, while the article was in the wrong version at the time you wrote this post, you say that "it has long needed correction", which suggests you have seen its correct version. In that case, references exist for a reason. -- Meni Rosenfeld (talk) 11:37, 17 January 2008 (UTC)
 * Apologies to Meni Rosenfeld. Somehow I missed picking up the fact that the erroneous version had only been there for eleven hours.  I had looked at a version from November which had the same error, and assumed (wrongly) that the error had been there since then.  If I had looked more carefully at the history I would simply have reverted the vandalism and left it at that.  I can see that many hours of work have gone into ensuring the accuracy of the article, so I will not make any changes, except to comment here that Euclid originally used "trapezium" to mean a general convex quadrilateral not necessarily having any parallel sides (but including all others quadrilaterals), then from about 1700, the word began to be used in England for the quadrilateral with one pair of parallel sides, and this usage gradually became dominant in the UK.  Use of the term "trapezoid" is rare in the UK, but it is normally used in the US sense when it does appear.  The last use of "trapezoid" to mean a general convex quadrilateral with no parallel sides was by R F Burton in 1851 (as far as I can determine).  Perhaps someone can correct me if I am wrong. Because current British and Commonwealth usage has "trapezoid" in the US sense (as a synonym for the UK "trapezium"), I feel that a slight adjustment to the article would help to clear up continuing confusion.  Again, apologies to Meni Rosenfeld who obviously feels deeply about this subject.    d b f i r s   14:04, 17 January 2008 (UTC)
 * P.S. Would you like some references to contradict your fallacious reference? Trapezoid definition (Only the table is wrong!)   d b f i r s   14:11, 17 January 2008 (UTC)
 * Huh? Everything on that page (which is in any case less reliable then mine) agrees with the article, so I'm not sure what your point is. This leads me to wonder which parts, if any, of your post are sarcastic. If you can find a reliable reference that contradicts the article you can edit accordingly.
 * I don't feel deeply about this subject. I only feel deeply about people who don't bother to think half a second before making nonsensical edits (like the recent one by anon). -- Meni Rosenfeld (talk) 15:40, 17 January 2008 (UTC)
 * Sorry, I'm not communicating very clearly, am I? I was apologising for my error in suggesting that the reversed terms had been there for some time, when in fact it was just vandalism or thoughtless editing that had appeared repeatedly.  You corrected the vandalism and I am happy with that, and I agree with your opinion of those who make alterations without thinking.  My only query was over British usage of "trapezoid".  In fact, nearly all British and Commonwealth usage is the same as the US meaning.  The table which you quote as reference suggests that the usage is the opposite in the UK for "trapezoid", when in fact it is only "trapezium" which has a different meaning.  I will collect together some reliable references (I agree the "mathopenref" is less reliable than your page).  Best wishes, and I am not arguing with you or being sarcastic, just trying to express the truth as clearly as possible, which I hope is what all true Wikipedians aim to do.   d b f i r s   17:49, 17 January 2008 (UTC)
 * Okay. You are no doubt familiar with Verifiability, so finding reliable sources to back up your claim is crucial. -- Meni Rosenfeld (talk) 17:58, 17 January 2008 (UTC)
 * Thanks, I'll take care. By the way, from your knowledge of US mathematics, do you know whether the US term "trapezium" normally includes concave quadrilaterals, or is it reserved for just the convex variety which do not satisfy other criteria?  (Genuine question, not trying to catch you out or anything!)   d b f i r s   19:38, 17 January 2008 (UTC)
 * I actually never claimed to have any knowledge of US mathematics, and indeed I have none. According to definitions such as the Merriam-Webster one, it seems to include concave quadrilaterals as well, but your guess is as good as mine. -- Meni Rosenfeld (talk) 19:47, 17 January 2008 (UTC)
 * Thanks, and sorry again for jumping to conclusions (based solely on your use of US sources and references). I'll leave you in peace to get on with valuable editing.    d b f i r s   20:25, 17 January 2008 (UTC)

Set or pair?
Why did we change pair to set? I always thought that a pair was a set of two, and thus pair would give a more precise definition. Have I missed some subtlety? '' d b f i r s   08:28, 14 April 2008 (UTC)
 * Since no-one has objected, and two other editors have agreed in the past, I am making the change. Dbfirs (talk) 07:24, 21 April 2008 (UTC)

History of the two terms
We still seem to be disagreeing over usage. Would it be better to combine the two paragraphs about definitions and usage, and put them after the introduction. The history is very confusing because both words have been used with both meanings in the past in British usage. Here is the history, for what it's worth:

Euclid used the word trapezium (in Greek, of course) to described all quadrilaterals more general than the parallelogram. Marinus Proclus (410 to 485 AD approx) in his Commentary on the first book of Euclid’s Elements invented the word translated trapezoid to refer to a general quadrilateral having no special properties. In 1788, Taylor’s translation of this commentary was published, including the sentence: “Of non-parallelograms, some have only two parallel sides, ... others have none of their sides parallel. And those are called Trapeziums, but these Trapezoids.”

In his Mathematical and Philosophical Dictionary, published in 1795, Charles Hutton seems to have misunderstood the order of Proclus’ sentence, for he defines Trapezium as “a plane figure contained under four right lines, of which both the opposite pairs are not parallel. When this figure has two of its sides parallel to each other, it is sometimes called a trapezoid”. This usage seems to have been adopted by both British and American mathematicians. Towards the end of the 1800s, British usage seems to have reverted to Proclus’ original definitions, and the term trapezium is regularly used for a quadrilateral with one pair of parallel sides throughout Britain. Dictionaries published around this time also have trapezoid defined as a quadrilateral having no parallel sides, but this usage seems to have died out in the UK (except in dictionaries where historic usage is recorded). The OED records this definition, saying only “Trapezoid (no sides parallel sense) Often called by English writers in the 19th century”. The term "Trapezoid" is now seldom if ever used by British mathematicians and is not normally taught in British schools. Modern usage is usually adjectival, and refers to parallel sides.  D b f i r s   01:45, 8 December 2008 (UTC)

Congruent
An anonymous editor keeps changing "equal" to "congruent" in this and other articles. In my view, the simpler word "equal" is clearer. What does anyone else think? (Also, most mathematicians define "trapezoid" to include parallelograms. I thought this was adequately explained in the article?).  D b f i r s   08:47, 10 January 2009 (UTC)

a trapezoid  has  4  —Preceding unsigned comment added by 68.104.91.19 (talk) 00:29, 21 January 2009 (UTC) the thing also is that the trapaziod does not have two right angles —Preceding unsigned comment added by 190.11.236.154 (talk) 17:15, 29 April 2009 (UTC)

hsfkidsoughdsigdsbhn green iz cool

Mathematicians use the word equal to mean things that are equal, not to mean things that have a property in common. When you say that a is equal to b, you mean they are the same thing. In the case of geometry, that means that they are the same shape (at the same place). When two things are not in the same place, but share a common property another word may describe the relationship better. In the case of Geometry, we use the word "congruent" to indicate when two things are different, but have the same property (which is supposed to be a property that is reflexive, symmetric and transitive). For example, segments may be different (not equal, as in two sides of a triangle) but have the same length (congruent, as in an isosceles triangle). In other words, it is incorrect to say that two sides of a triangle are equal, but say that two sides of a triangle are congruent. Common usage, however incorrect, uses the word "equal", not "congruent". However, wikipedia is not a compilation of common usage language, it is an encyclopedia, and as such, it should use the proper language. Therefore, the word congruent (with a link to the explanation of the word) should be used when appropriate.
 * The purpose of Wikipedia is to communicate in language that most readers understand. Use of the word congruent for angles introduces concepts of superposition which are self-evidently false for angles in many triangles (depending, of course, on which sense of the word angle you intend).  The existing phrasing (using equal in measure and equal in length) avoids confusion and should satisfy usages on both sides of the pond.  Your extended use of the word congruent is not common in the UK.  Is it universal in the USA?    D b f i r s   08:08, 16 August 2009 (UTC)
 * I think you need to read on what angles are, take a book on advanced geometry. There is no concept of superposition (in fact, that was one of the goals of the axiomatization of geometry, to get rid of notions like superposition in its axiomatization). The word congruent can be used consistently, even for angles. Take a look at the work by Hilbert in Foundations of Geometry.

Also arguing that the purpose of Wikipedia is to for it to be accessible is quite honorable, but you can not use words like "equal" when "equal" is not what is meant. I would not try to shield in that principle, but in the principle that readers have to be aware that there is a word that describes the relationship. It is a matter of proper language. Please read a bit about axiomatic geometry to see that there is no contradiction on using the word "congruent". —Preceding unsigned comment added by 72.178.193.150 (talk) 18:18, 23 August 2009 (UTC)
 * There is on-going discussion about what angles are, and different people define the word in different ways. In UK schools, an angle is defined as an amount of turn, so equality is clearly possible.  A very small percentage of Wikipedia users have read Hilbert.  The word "congruent" as applied to angles is very confusing (and apparently false) to those who have been taught in the UK, whereas the word "equal" is clear and unambiguous because of the long tradition of teaching Euclidean Geometry.  The situation in parts of the USA seems to be the reverse.  Do school students in the USA read Hilbert?  Professional mathematicians need to remember that this is a basic article.  This does not mean that it needs to be imprecise in its use of language, but it does mean that obscure senses of words must be avoided.  I think that the current article reflects this compromise.    D b f i r s   06:32, 24 August 2009 (UTC)
 * Please read Hilbert and then revise your words. The main point is that what is taught is schools and what something really is may be different. Knowledge has advanced, we now know better than Euclid ever did. An angle is a set, not a number. An angle has a measure, which may be equal to the measure of another angle without the angles being equal (the same set). Do not shield in what you were taught. That has changed. It changed before you were taught, but the change in perception takes time (geez, I still think sometimes it is the sun going around the earth). Please do a favor to those that want to learn right and explain things as they really are, not as they were explained two thousand years ago, when they were written not as well as we write them today. —Preceding unsigned comment added by 72.178.193.150 (talk) 01:57, 5 October 2009 (UTC)
 * You will find that the meaning of the word angle is still under discussion amongst mathematicians. Even in the USA, not everyone seems to agree with your view.  (and in fact the sun and the earth orbit a common centre of gravity)  I think the various articles in Wikipedia that refer to equality (or congruence) of angles use the phrase "equal in measure" which is easily understood on both sides of the Atlantic, and allow for the different interpretations of the definition of "angle".  We, on this side of the Atlantic, also want to "learn right", but we do not always adopt the edicts of American educators.    D b f i r s   20:58, 21 October 2009 (UTC)

Inconsistency
We have a serious inconsistency in the labelling of sides. The diagram and one formula has parallel sides "a" and "b", but the other formulas (formulae) have sides labelled consecutively, with parallel sides "a" and "c". Since the latter seems more "standard", I suggest that we change the diagram and the area formula. Alternatively, we could use p & q (or p1 and p2) for the parallel sides, and $$\ell$$ and m (or $$\ell$$1 and $$\ell$$2) for the legs, (then d1 and d2 for the diagonals). What does anyone else think?  D b f i r s   07:41, 1 September 2009 (UTC)
 * All seems OK now, and we seem to have standardised on using a & b for the parallel sides and c & d for the other two. This is fine as long as we are consistent.    D b f i r s   14:50, 5 June 2010 (UTC)
 * I see that the error crept back, but Circlesareround has corrected it. Thank you.    D b f i r s   11:09, 21 February 2013 (UTC)

Hatnote template
Hi, TenPoundHammer and CBM. I did change the template. Even twice, because I did not read CBM's rv (which made mine a bad revert). Now please cool down: I have proposed other uses6 at TfD just now. We don't need edit warring, the grand thing will be Good Hatnotes. -DePiep (talk) 00:35, 17 January 2011 (UTC)

Canadian English left out
"trapezoid in American English and as a trapezium in English outside North America."

North America comprises Canada. But American English does not include Canadian English. HTML2011 (talk) 02:06, 23 February 2012 (UTC)


 * Do you use both terms for the same shape in Canada? This is the case in Australia, and increasingly true in the UK, though "trapezium" is still by far the most common term used here.    D b f i r s   07:03, 10 September 2012 (UTC)


 * Presumably that sentence was written by someone who could not confidently say what is the usage in Canada. —Tamfang (talk) 18:54, 10 September 2012 (UTC)


 * I added that Canadians use "trapezoid". Trapezium is almost unheard of in Canada. Nutster (talk) 14:52, 12 January 2014 (UTC)


 * Thanks for confirming that. I assume that many Canadian schools use American text books and that British schoolbooks are not seen there.    D b f i r s   22:08, 12 January 2014 (UTC)


 * Speaking as a Canadian, we usually write our own textbooks, but when we do get foreign books, it is a lot easier to get books across a great big land border than a few thousand kilometres of ocean. The other point on this is that us Canadians tend to get more American television and radio broadcasts than British, so we often use American terms when they are not homonyms.  See the article on Canadian English.  Nutster (talk) 16:12, 14 March 2014 (UTC)


 * Thanks for the link to the article, which confirms my impression (gained from my cousin who spent most of his life in Canada) that Canadian vocabulary mainly matches British usage rather than American, with the notable exception of words connected with the motor industry. That's why I was surprised that you use "trapezoid" instead of "trapezium".  Thanks for clarifying the article.  There are probably other exceptions to my "rule", and a lot of regional variation close to the border.    D b f i r s   21:51, 14 March 2014 (UTC)

Russian italic Cyrillic
Is there any chance of changing "Russian трапеция" to use oblique rather than italic, or even plain "Russian трапеция", as the first letter would then look more like the Greek τραπέζιον from which it comes. Rumping (talk) 08:10, 23 April 2012 (UTC)


 * In my default font (Lucida), т looks like 'т'. I infer that to you (in what, Helvetica?) it looks like m? —Tamfang (talk) 18:56, 10 September 2012 (UTC)

Scalene trapezoid ?!?
Is a scalene trapezoid a trapezoid with all sides non-congruent (as currently in the article), or with just the legs non-congruent? For example, a trapezoid that is not right and is not isosceles, but which has one of the basis congruent to one of the legs, would not be scalene according to the current article. Is that ok? Can anyone add a trustworthy source to the scalene trapezoid definition? — Preceding unsigned comment added by 84.203.43.58 (talk) 21:49, 12 January 2013 (UTC)


 * The current article says "no equal sides" which sounds correct to me. A trapezoid can be both scalene and right-angled, and one which has a base equal in length to a leg would not be scalene.  I haven't heard of any other definition, but if anyone else has, then please post a ref here.  I can see why there is confusion, because it is possible to draw a trapezoid that is neither scalene nor isosceles.  Would it be better to completely remove the sentence in the lead, because there is no "contrast"?  I'm not sure that "scalene" is a useful concept for trapezoids.    D b f i r s   08:19, 13 January 2013 (UTC)

I noticed the "no equal sides" seems to be the most recurrent definition, searching on various web-sites. Though, ony a few people define it by saying that only the legs (or equivalently, the non-parallel sides) should be different (e.g., http://www.mathcaptain.com/geometry/types-of-quadrilaterals.html or http://forgettingalzheimers.wikispaces.com/file/view/Trapezoids.ppt/129860685/Trapezoids.ppt), others characterize a scalene trapezoid as deriving from cutting a scalene triangle parallel to the bases (similarly to isosceles trapezoid, obtained from an isosceles triangle). Therefore, it would be nice to at least check one or a couple of reliable sources, if any, on such topics. For example, an Italian definition by Treccani (http://www.treccani.it/enciclopedia/trapezio_%28Dizionario-delle-Scienze-Fisiche%29/) talks about only non-equal legs, where Treccani is a very well-known (printed) encyclopedia throughout the country (though, not sure that the on-line dictionary can be considered equally reliable as the traditional printed volumes).

Midsegment and height
The recent addition to this section (deriving the height in terms of sides) uses a different labelling of sides. If this addition is worth keeping, then the new diagram needs to be modified to match the earlier convention in the article, or the remainder of the article needs to be modified to match this new diagram. Any preferences? ( ... or would it be better to delete the derivation of the formula?)   D b f i r s   22:01, 12 July 2016 (UTC)


 * About the cancelled proof: This is an encyclopedia, that is, a collection of results and information. No other formula is derived in the main page, so why put in a proof of that height formula? There are exceptions, for instance Heron's formula, which is on one topic. But if we start putting in proofs to every formula this will not be an encyclopedia but a math book, and that is not the purpose here! That is another project. If the proof of the height formula shall be included in Wikipedia, please create a new page, called for instance "Trapezoid height". There this proof is appropriate, and it shall then be linked in the main page. Circlesareround (talk) 06:57, 15 July 2016 (UTC)


 * Response about proof cancel: I understand what you're saying. However I think it may be wise of you to take the context into consideration. First, yes this is an online encyclopedia, but it is not bound by the length considerations of a paper encyclopedia so putting more useful information is unlikely to harm anyone, and likely to help someone. Second, yes there are no other proofs on the page, the reason to include this one is that it is brief, easy and derives a fundamental feature of the object in question. Third if this "turned into a math book" how would this somehow be of harm to those that are looking for an encyclopedia? They can search, they don't actually need to print the thing out... Finally, this is Wikipaedia, and the page on the Trapezoid; probably 75% of the viewers are elementary school kids. I'm sure the analysts among us are visiting different pages. I think that the young children who are most likely the consumers of this page would benefit from a quick proof, while analysts may be clever and patient enough to skip it. That aside, I'm fine with your suggested solution of making a separate page. I'll make one and link to it from the main page. Overall I think that too much information (if factually correct and relevant) given the fact that this is not a medium where space is a scarce resource is the better compromise. darkhipo (talk) 07:24, 15 July 2016 (UTC)


 * I'm neutral about inclusion on this page, but it could not remain in that form because it used a different naming of sides. Perhaps a separate article is best, then the diagram can still be used without alteration.    D b f i r s   08:40, 17 July 2016 (UTC)

The definition again
There is, as is well explained in its own section, a difference between the exclusive definition (there is exactly one pair of parallel sides) and the inclusive definition (there is at least one pair of parallel sides). We are in the midst of a transition period where the older exclusive definition is being replaced by the inclusive one. Both definitions can be found on the web and in textbooks. I grew up with the exclusive definition, but I now see that the commoncore K-6 geometry recommendations incorporate the inclusive definition. It has long been true that college level geometry courses have been using the inclusive definition and now there is some hope that the grade schools will catch up to them. A few authors have hedged their bets on this issue, such as Eric Weinstein. He defines a trapezoid as a quadrilateral that has two parallel sides. Notice that he does not say "exactly" two, in fact, he makes no statement at all about the other two sides. It is quite proper then to paraphrase his definition as "at least two parallel sides" in keeping with the knowledge that the inclusive definition is preferred beyond grade school. If you insist on using the exclusive definition then it seems to me that you need to have a very good reason for claiming that a square is not a rectangle, which is the statement parallel to "a parallelogram is not a trapezoid".--Bill Cherowitzo (talk) 03:39, 27 May 2017 (UTC)


 * We've "always" used the inclusive definition on this side of the pond (except we call it a trapezium, of course). I wrote "always", but then remembered that Euclid had a different meaning.  I've added another reference to counter the claim of our anon editor.   D b f i r s   03:48, 27 May 2017 (UTC)

Here is a use for a trapezoid.
http://www.larouchepub.com/eiw/public/1995/eirv22n09-19950224/eirv22n09-19950224_050-garfield_the_pythagorean_theorem.pdf John W. Nicholson (talk) 01:01, 27 November 2017 (UTC)

Wrong claim about exclusive definition
This page stated that under the exclusive definition, a trapezoid would be determined by the length of its sides whereas a parallelogram would not be and that this makes trapezoidal approximation ill-defined. This was given with no source. I don't see how the inclusive definition would make trapezoidal approximation ill-defined. Provide a source or proof or leave it out. — Preceding unsigned comment added by 2601:5C0:C100:FC:BDD5:C4FE:F1DB:6F27 (talk) 22:17, 2 March 2020 (UTC)

Etymology: it's a mess.
"Marinus Proclus" never existed, it's two different people! Marinus was a student and biographer of Proclus. Judging by the quoted work (primary source, Proclus' commentary on Euclid's Elements), Proclus did use "trapezoid" as being different from "trapezium". Marinus probably slipped into the article by mistake. But did he? The indicated secondary source, OED, is only accessible to subscribers, so I didn't outright remove Marinus from the article. Arminden (talk) 11:07, 21 March 2020 (UTC)

After stating that the form "trapezium" is more commonly used than "trapezoid", 5 examples are given, none of which seem to support the statement. All of the examples stop short of either ending, the "m" or the "d". MarkGoldfain (talk) 17:37, 11 June 2020 (UTC)

Requested move 21 June 2021

 * The following is a closed discussion of a requested move. Please do not modify it. Subsequent comments should be made in a new section on the talk page. Editors desiring to contest the closing decision should consider a move review after discussing it on the closer's talk page. No further edits should be made to this discussion. 

The result of the move request was: Page moved. Moving article back to its original title Trapezoid as it was moved without discussion. (closed by non-admin page mover) Jerm (talk) 01:17, 29 June 2021 (UTC)

Trapezium and trapezoid → Trapezoid – Article is in American English, and per WP:OTHERNAMES there may only be one title. Besides the greater overall popularity of American English, Trapezium doesn't even redirect to this page as it has two contradictory meanings and means something else entirely in American English. Trapezoid redirects to the present article. Until recently,, this article was at Trapezoid. Eostrix  (&#x1F989; hoot hoot&#x1F989;) 15:59, 21 June 2021 (UTC)
 * Support. "Trapezoid" is the term we always learn when we learn the kinds of shapes. Georgia guy (talk) 16:24, 21 June 2021 (UTC)
 * Hmm. The two names are intended to allow for the inclusion of both Trapezoids (a.k.a. Trapeziums, i.e. with ONE set of parallel sides) and Trapeziums (a.k.a. irregular quadrilaterals, or Trapzoids, i.e. with NO parallel sides); the latter isn't covered in detail anywhere in the encyclopedia currently. Dealing with them together has the benefit of avoiding the confusion caused by the contradictory naming conventions, as explained in the etymology section.
 * Onceinawhile (talk) 16:34, 21 June 2021 (UTC)

The discussion above is closed. Please do not modify it. Subsequent comments should be made on the appropriate discussion page. No further edits should be made to this discussion.
 * Support – The current title (from a move yesterday) has inappropriate capitalization and unnecessary conjunction form, based on a brief discussion where some think these are different things and some think they are the same think in two different varieties of English. It would have been better to just revert to the stable title and discuss from there. Dicklyon (talk) 17:24, 21 June 2021 (UTC)
 * Support. User:Onceinawhile's idea to treat two different topics in a single article because they have names that are commonly swapped for each other goes against the advice in WP:NOTDICT to focus articles on single topics, and not on the words used for those topics. —David Eppstein (talk) 17:49, 21 June 2021 (UTC)
 * , I see it like Enclave and exclave, Proper and common nouns and Id, ego and super-ego. The fact that it would also help readers with the terminological confusion is just a side benefit. Onceinawhile (talk) 18:12, 21 June 2021 (UTC)
 * , those are not synonyms at all. The only difference between trapezoid and trapezium is that the former is the American term and the latter is the British term. Thus, it is a bad analogy. An analogy would be having the color article at colour and color. Georgia guy (talk) 18:15, 21 June 2021 (UTC)
 * , please read the etymology section. Trapezium and Trapezoid and NOT synonyms in American English (the language of the article). They are two similar and related concepts. Onceinawhile (talk) 19:48, 21 June 2021 (UTC)
 * An even more appropriate analogy would be to have merged the articles Columbia blue and Blue while leaving all the other blue colors as separate articles. You have attempted to make an article that is simultaneously about general quadrilaterals, and about quadrilaterals with two parallel sides, while leaving all of the other quadrilaterals as separate articles. What a disorganized way of thinking about this topic. —David Eppstein (talk) 07:19, 22 June 2021 (UTC)
 * I wouldn't call it disorganized, as it is organized by English etymology, but Wikipedia is not a dictionary.-- Eostrix  (&#x1F989; hoot hoot&#x1F989;) 07:23, 22 June 2021 (UTC)
 * Support per nom - although the move should have been simply reverted without an RM, as this relatively prominent article will now be stuck with an obviously erroneous title for a week. Lennart97 (talk) 18:42, 21 June 2021 (UTC)
 * Comment. Please let us wait until someone other than User:Onceinawhile says oppose. before we can label this as a move that we can't speedy close as moved. Georgia guy (talk) 19:04, 21 June 2021 (UTC)
 * , I would like to wait until commentators have made the effort to fully understand what they are discussing. I agree with Lennart97’s point about process; this could have been reverted without an RM. The good news is that more eyes on the situation might help come up with a good solution that everyone is happy with. Onceinawhile (talk) 19:51, 21 June 2021 (UTC)
 * Support The title is more confusing now than it was before; the old title should be restored. XOR&#39;easter (talk) 18:23, 22 June 2021 (UTC)
 * Support. Restore the status quo ante. Srnec (talk) 02:54, 23 June 2021 (UTC)
 * Oppose. 1) No evidence has been provided for the "the greater overall popularity of American English" (particularly with regard to trapezoid over trapezium anyway), 2) the fact that Trapezium doesn't redirect here is irrelevant when the question is the most common name for this mathematical object (all that proves is that trapezium is perhaps also a common name for something unrelated, and 3) the fact that it means something different in American English also isn't relevant if the usage in British English is sufficiently common. None of this is to say that the article should remain at it's current title, or that it should be renamed trapezium instead - I am simply unpersuaded by the evidence/arguments that trapezoid is in more common usage. I wouldn't be surprised if either trapezoid or trapezium were actually more common, but that's something that must be demonstrated, not asserted. 86.130.90.78 (talk) 00:34, 28 June 2021 (UTC)

otherwise there are two pairs of bases
In that case isn't it a parallelogram? — Preceding unsigned comment added by 2A02:2788:1008:6D6:E2CB:4EFF:FE88:1A2D (talk) 19:27, 28 January 2022 (UTC)

How do we deal with the difference between North American English and the rest of the world?
A discussion started at Teahouse about this article, with pointing out that the terms "Trapezoid" and "Trapezium" have interchanged meanings between North American English and British English, meaning that this article can never keep both groups happy. Although the problem is inevitable, I do think the effects, the confusion inflicted on readers, could be mitigated. Here are a few of the problems: (1) This article, whose title is "Trapezoid", begins "In English outside North America, a convex quadrilateral in Euclidean geometry, with at least one pair of parallel sides, is referred to as a trapezium", which is confusing to the North American reader. The lead of an article about "X" normally begins by saying "A thingumy with whatsits is called an X", not "A thingumy with whatsits is called a Y by some other group of people", where the reader knows that Y is absolutely not an X, and has spent half their childhood learning the difference. (2) The article then tries to clarify this by introducing a table with examples, a very good idea. But unfortunately it simultaneously introduces a second issue of nomenclature, whether names should be inclusive or exclusive (in the sense that a square is a specialised sort of rectangle, so we could define a rectangle as including all squares as well as rectangles with different side-lengths, or we could define it as excluding the special case of the square). As a result, the table is quite confusing. I'm not going to boldly make changes, because this is an emotive area, and also an area where every reader will perceive the text differently, and so it's important to operate by consensus. Instead, I'm suggesting the following possible changes (not all of them, they're just possibilities): (1) Rename the title to "Trapezoid (North American)" or similar, to emphasise which definition is in use. (2) Start the article with text to make the situation clear:
 * A quadrilateral with at least one pair of parallel sides is called, in American and Canadian English, a trapezoid. In British and other forms of English, a (North American) trapezoid is called a trapezium. This article uses North American nomenclature. The transposition of these two terms was a result of an error in Charles Hutton's mathematical dictionary

(3) Remove the attempt to explain the difference between exclusive and inclusive from the table in "Etymology", since it isn't brought up until the section below. To be honest, I personally think that over-emphasising the difference between inclusive and exclusive is unhelpful. The reader will probably be quite able to grasp the idea that a parallelogram does everything that a trapezoid does (and more). The text version in the paragraph about exclusivity is probably quite sufficient without the table. Of these ideas, I think (2) and (3) are my favourites. The disambiguation page for Trapezium does a good job of helping the British English speaker who's hunting for the right article. Any thoughts Elemimele (talk) 18:23, 2 April 2022 (UTC)


 * I really like all the suggestions. They reduce confusion for both North American and non-North American English speakers. (2) is definitely a must, and so is (3), (1) is also pretty good. Lone Warrior 007 (talk) 00:41, 3 April 2022 (UTC)
 * (2) is seriously needed, I think (1) is slightly redundant if (2) is done (as I also don't see the word "trapezoid" in British English as much anyway). Joseph2302 (talk) 12:58, 4 April 2022 (UTC)
 * We shouldn't try to solve this disambiguators in the article title. Support (2), though. I also think we should put File:Trapezium-trapezoid-comparisons.png (currently on Trapezium) somewhere toward the top of this article. - MrOllie (talk) 13:21, 4 April 2022 (UTC)
 * From the above, I am assuming the consensus is to change the wording of the lead, which I've done. I agree,, that would be a most helpful picture. I tried to put it in, but it just appeared on the right hand side, very small, underneath the existing info-box, where it wasn't very visible. So I'll leave that to someone who's better at Wikipedia picture formatting. Changing the title seems unnecessary and unwanted. I'm still in favour of simplifying the table by removing the inclusive/exclusive thing, but Wikipedia table-formatting scares me. I might have a go, but I'll do it as a separate edit whenever I try, so it's easily revertible if the change isn't popular. Elemimele (talk) 10:12, 8 April 2022 (UTC)

Requested move 21 September 2022

 * The following is a closed discussion of a requested move. Please do not modify it. Subsequent comments should be made in a new section on the talk page. Editors desiring to contest the closing decision should consider a move review after discussing it on the closer's talk page. No further edits should be made to this discussion. 

The result of the move request was: not moved. (closed by non-admin page mover) GeoffreyT2000 (talk) 03:34, 29 September 2022 (UTC)

Trapezoid → Trapezoid and trapezium – This article covers both quadrilaterals with parallel sides (trapezoids) and quadrilaterals with no parallel sides (trapeziums). To be clear, this proposal is not about the British-American terminology difference. It is about the fact that (American) trapeziums (i.e. quadrilaterals with no parallel sides) is within the scope of this article, so should be represented in the title. Please could commenters avoid the quagmire of the terminology question and focus on the scope. Onceinawhile (talk) 20:42, 21 September 2022 (UTC)
 * Oppose. Nonsense. Not everyone knows what a trapezium is. Georgia guy (talk) 21:13, 21 September 2022 (UTC)
 * I have clarified in my post above. Onceinawhile (talk) 07:29, 22 September 2022 (UTC)

The discussion above is closed. Please do not modify it. Subsequent comments should be made on the appropriate discussion page. No further edits should be made to this discussion.
 * Comment and opposition: My comment is that the lead section of the article does not seem to even mention the American meaning of trapezium. That shortcoming combines with the WP:ENGVAR issue to make this RM difficult to understand. My opposition is because, as far as I know, Wikipedia does not ordinarily identify two different topics in its article titles in this sort of "Topic A and topic B" format. Looking at the article content, the article seems primarily focused on trapezoids, not trapezia/trapeziums). Its only discussion of trapezia is in the context of explaining the transatlantic differences in terminology. All of the discussions of properties (e.g. the sections about "Midsegment and height", "Area" and "Diagonals", and most of the others too) seem to be about the case with two parallel sides and thus are about trapezoids (assuming I understand the terminology correctly). So the article really seems to be about trapezoids, only discussing trapezia since that is a topic closely related to trapezoids. There doesn't seem to be a lot we have to say about trapezia. I also note that in the previous "Requested move 21 June 2021" discussion, there was more support expressed for the current title than for a similar "Topic A and topic B" title. —&#8288;&#8202;&#8288;BarrelProof (talk) 19:12, 23 September 2022 (UTC)

Why AE over BE?
In many cases, terms indicating a geometrical shape that use the suffix -oid are connected to *3D, not 2D shapes*: solenoid, cuboid, ovoid... Therefore, the AE term "trapezoid", as opposed to the BE "trapezium", is confusing to non-AE speakers. AE often tends to have unexpected pecularities, while BE is closer to philological developments in other European languages of wide circulation; BE is therefore better suited for non-native speakers, as a lingua franca. This, on top of the geographical area of use and the number of users, should give BE a preferred role in Wikipedia articles on topics not specifically related to the USA. In this case, Canada uses the US term, but that's not even a general rule, as Canada sometimes uses the original, BE version of words. Arminden (talk) 11:09, 21 March 2020 (UTC)
 * Agreed. The article also refers to the almost exclusive use of the term trapezium outside of the US & Canada, so it's silly to have the article be named a term a vast minority use. I propose changing the title to Trapezium. Getsnoopy (talk) 17:54, 2 July 2020 (UTC)
 * I have done some work to fix the confusion here, including Arminden's point in the etymology thread immediately above this, but have not changed the AE to BE as this should probably be more widely discussed.
 * I have moved the title to incorporate both definitions as they are frequently used in comparison to each other, and we don't have an article on the other. Onceinawhile (talk) 20:26, 20 June 2021 (UTC)

I agree with this point, trapezium is the global, international standard word for this shape. Trapeziums as a subset of trapezoids makes intuitive sense from an understanding of the -oid suffix, and the article itself says that the trapezium <-> trapezoid swap was the result of an error. Mtjh (talk) 20:29, 3 December 2022 (UTC)

All European languages follow Proclus's structure ...
It may worth mentioning that some other (non-english) schools make distinction between the two terms, they have different words for the "inclusive" and "exclusive" definitions. We learned in Romania (albeit that was 30-40 years ago, I don't know what they teach nowadays) that a "trapezoid" (same Romanian word as in English) includes all squares, rectangles, rhombuses, etc, same way as a "cuboid" (idem) includes all parallelepipedic structures, while a quadrilateral with two and only two parallel sides (a "pure trapezoid") is called "trapez", same as a "pure" cuboid is called cube (Romanian: "cub"). Some guy with a better English skill may add that mention. LaurV (talk) 02:18, 2 June 2023 (UTC)

parallel sides implies convexity
I'm not proposing any change, just observing that a quadrilateral with parallel sides cannot be concave. So this criterion is superfluous. Twixter (talk) 15:50, 27 March 2022 (UTC)


 * Nope. You have to add non-self-intersection, to imply convexity. LaurV (talk) 02:26, 2 June 2023 (UTC)

"Proper trapezoid"
Some sources use the term "proper trapezoid" to specifically talk about the exclusive case of non-parallelograms (such as this page), which is consistent with other uses of the adjective (such as proper class) to filter the definition to exclude a specific subtype of the inclusive definition. Why isn't this mentioned anywhere in this article or anywhere else in Wikipedia? 104.175.74.27 (talk) 03:43, 4 June 2023 (UTC)
 * Added this due to lack of objections. 104.175.74.27 (talk) 03:40, 10 June 2023 (UTC)

Special cases
Something is off with the. Acute, right and obtuse trapezoids are three different kinds of trapezoid, yet the rectangle is both a special case of right and obtuse trapezoid, and the square is a special case of the three. --2803:2A00:2C10:7E41:6C14:C6A9:37B:3389 (talk) 18:47, 9 December 2023 (UTC)