Talk:Trapezoid

Median formula by similarity

Median of a trapezoid

If I am not mistaken, the median of a trapezoid can be obtained by similarity, involving one of the trapexoid's legs other than two bases. Here $EG$ is the median. Finding $EG$ is $${\frac {AB\times DE+CD\times AE}{AE+DE}}.$$ @David Eppstein, @Jacobolus, did this formula appear in US junior or high school? Dedhert.Jr (talk) 08:27, 11 March 2025 (UTC)

I don't think anyone other than a schoolteacher is likely to remember precisely which methods for deriving particular formulas appear in school. If you hunt in textbooks you can see for yourself how they usually explain/prove these kinds of metrical identities. –jacobolus (t) 13:21, 11 March 2025 (UTC)

@Jacobolus. I mean, would it be fine to include this, as long as there is a reliable source, even though it uses other languages than English? Dedhert.Jr (talk) 13:32, 11 March 2025 (UTC)

Are you asking whether we need a geometric proof for the formula $m={\tfrac {1}{2}}(a+b)$? Probably not, but what did you have in mind? –jacobolus (t) 13:44, 11 March 2025 (UTC)

I didn't ask for geometric proof for that formula. I'm asking for including another formula, which is used from another. I mean, there is a study of the formula I have mentioned earlier, so it is worth it for WP:NEUTRAL. But again, I prefer to hear the opinion. Dedhert.Jr (talk) 13:57, 11 March 2025 (UTC)

What's the point of this other formula / what's the context? I thought the point was to prove the midsegment length formula. Maybe you can elaborate on what you have in mind, or link your non-English source(s). –jacobolus (t) 18:54, 11 March 2025 (UTC)

Non-English sources? Yes I do have. But the sources are tertiary and websites. I am shocked that English sources never mentions this formula. The formula is related to the congruence ( I could somehow confused mentioning it with the similarity), where median divides the length of legs unequally. Dedhert.Jr (talk) 04:00, 13 March 2025 (UTC)

Trapezoid as a graphical symbol

I took out the following unsourced passage, which seems fairly marginal:

In computer engineering, specifically digital logic and computer architecture, trapezoids are typically utilized to symbolize multiplexors. Multiplexors are logic elements that select between multiple elements and produce a single output based on a select signal. Typical designs will employ trapezoids without specifically stating they are multiplexors as they are universally equivalent.

Someone might want to write more about trapezoids as a graphical symbol and include a slimmed down version of this particular example, but it would take finding sources and fleshing it out. –jacobolus (t) 13:36, 11 March 2025 (UTC)

Why not? Aside from the graphical symbols, trapezoids also used in the highways signs. I have found Ontario Highway 502. Dedhert.Jr (talk) 03:57, 13 March 2025 (UTC)

Characterizations vs. properties

I'm not sure how helpful it is to have these two sections separated. The characterizations of a trapezoid are all "properties", and many properties can be used as characterizations. Even if these sections are going to be separated, I'm not sure the characterizations section should come first; that order seems less accessible and helpful to readers. The § Condition of existence section probably also belongs under Properties somewhere. –jacobolus (t) 17:59, 12 March 2025 (UTC)

@Jacobolus I could only think of characterizations merged into the properties sections based on the elements (e.g. angles, diagonals, etc.) Condition of existence is probably the next subsection. Dedhert.Jr (talk) 03:55, 13 March 2025 (UTC)

Median of the trapezoid merge

As far as I can tell there has been no change here, so calling this a "merge" is a bit much. Also this notice doesn't need to be permanently at the top of this talk page. –jacobolus (t) 16:20, 21 March 2025 (UTC)

Etymology

The article would benefit from a discussion of the continued difference in terminology. There must have been some debate at the time British English mathematicians changed back to the world standard. Perhaps there has been some more recent discussion of why American English persists in using Hutton's definitions.

Humpster (talk) 23:16, 24 October 2025 (UTC)

Trapezoid as a parallelogram

Should we remove this sentence from the article, “If the trapezoid is a parallelogram, then the choice of bases and legs is arbitrary.” Because I think it is unhelpful, misleading and probably incorrect by saying a trapezoid can be a parallelogram. Isn’t the definition of a trapezoid is that they have to always have one parallel side? WikiGrower1 (talk) 22:06, 31 December 2025 (UTC)

Did you read the article? It is correct to say that a trapezoid can be a parallelogram. A trapezoid has at least one set of parallel sides. For a parallelogram, both sets of opposing sides are parallel, so it is a trapezoid, and either set can be considered the bases. The sentence you want to remove is perfectly correct. Meters (talk) 11:15, 6 January 2026 (UTC)