Talk:Trapezoid

"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 "special cases" image. 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)

Median formula by similarity

File:Trapezoid-midsegment-theorem-diagram.svg

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 $m=\frac{1}{2}(a+b)$? 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:

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 Template:Alink 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)