Talk:Isosceles trapezoid

message: What does "intersect at equal positions" mean? — Timwi 01:32, 8 Mar 2004 (UTC)
replies: text: A little late, but I think what is meant by this is that the two top sections of the diagonals are congruent, and the two bottom sections of the diagonals are also congruent. All four diagonal sections are not congruent, as can be seen by drawing a tall, skinny isosceles trapezoid. Loggie 01:29, 4 May 2005 (UTC)
thread_title:  "intersect at equal positions" 

message: Are you sure this is a stub? It seems a little long to be a stub yet too short to be a full-fledged article. --Mannyram24 13:36, 6 April 2006 (UTC)
thread_title:  A little long to be a stub 

message: I've moved the following paragraph from the article:
An isosceles trapezoid is also a quadrilateral such that the diagonals divide each other into segments of different length that are congruent among each other. In the picture above, this means that if AE = DE, BE = CE and AE\not=CE, then the quadrilateral is an isosceles trapezoid.
Whilst I understand what the anon editor was trying to say, I have two issues:  
# the phrase congruent among each other is vague, and so is not good mathematics. The property is also menioned earlier in the article.
# The condition AE\not=CE, is not necessary according to our definition.
What does anyone else think?  Dbfirs 08:22, 24 August 2009 (UTC)
replies: text: Well, if you do not like a phrase, improve it; do not remove it. More to the point, the condition AE\not= CE is given because trapezoids are not parallelograms. If AE = CE (and BE = DE), then the quadrilateral is a parallelogram, not a trapezoid. This brings me to the main point. The definition of isosceles trapezoid in this article is not the correct one. That definition is a property. More specifically, we can agree to study quadrilaterals that have a line of symmetry as stated in this article, but those are different type of quadrilaterals, not isosceles trapezoids. In other words, if you want to use such definition, do not use it to define isosceles trapezoids. To give a complete answer, an isosceles trapezoid is a trapezoid (as in "a quadrilateral that has only two parallel sides) where the non parallel sides have the same length. We can talk more about it, if you like.  —Preceding unsigned comment added by 72.178.193.150 (talk) 14:55, 30 August 2009 (UTC)
replies: text: It is considered improper, on talk pages, to edit the comments of others to reverse the meaning.Dbfirs 08:26, 31 August 2009 (UTC)

text: I've done as you suggest (with the help of Tamfang).  Dbfirs 08:28, 31 August 2009 (UTC)

text:  If AE=CE (and other defining conditions are met) it's a rectangle, which is an isosceles trapezoid and a parallelogram. —Tamfang (talk) 15:50, 30 August 2009 (UTC)
replies: text:  See my response above as to why to make isosceles trapezoids not be parallelograms.  —Preceding unsigned comment added by 72.178.193.150 (talk) 15:53, 30 August 2009 (UTC)
replies: text:  Um, obviously we don't want to define trapezoids as parallelograms, but you haven't stated a reason to define trapezoids in such a way as to exclude rectangles. —Tamfang (talk) 16:33, 30 August 2009 (UTC)
replies: text: Our article on quadrilaterals specifically shows rectangles as a subset of isosceles trapeziums (trapezoids in the USA).  I see no reason to exclude rectangles as a subset since rectangles inherit all properties of the isosceles trapezoid.  The current Wikipedia definition of the isosceles trapezoid seems to have been carefully constructed (five years ago) to precisely match the article on quadrilaterals.  Dbfirs 08:08, 31 August 2009 (UTC)
replies: text: The main idea is that trapezoid is the quadrilateral that you obtain when you divide a triangle in two by a parallel line to one of the sides (one is a similar triangle to the original triangle, the other a quadrilateral which is a trapezoid). Point is, the trapezoid was not supposed to be a parallelogram. Parallelograms, instead have  a different idea behind them. There is no such thing as a trapezoid that is a parallelogram (or viceversa). Of course, you can define things to your convenience so that rectangles be trapezoids, but what have you gained from it? The theory has not been improved, has been made more confusing. Particularly, for those poor souls that do not really understand what is really going. It seems that I can't win just because you refuse to hear. I wish you had a better reason than what you are giving. Really. I really wished I could learn something other than sometimes you loose because the person in power does not listen. To summarize, the definition is wrong. It leads to more problems than it solves. I am sorry you were not better advised at the time the definition was written. Enough.72.178.193.150 (talk) 02:09, 5 October 2009 (UTC)
replies: text:  I see a difference between "If you do this you get a trapezoid" and "A trapezoid is what you get if (and only if) you do this".  The definition of a geometrical figure ought to be its properties, not its construction (there's more than one way to construct anything). — Please note that a rectangle can be made from a degenerate isosceles triangle with a vertex at infinity.  —Tamfang (talk) 15:16, 19 October 2009 (UTC)
replies: text: The inclusive definition given in the article (and in the quadrilateral article) is the one that is standard in the UK, but I think American mathematicians avoid the exclusive definition for their trapezoids (our trapeziums).  It is probably not important enough to argue about.  Dbfirs 11:27, 23 May 2010 (UTC)
thread_title:  Paragraph moved from article 

message: In Euclidean geometry, an isosceles trapezoid (isosceles trapezium in British English) is a trapezoid where the legs have equal length.
Under this definition, a non-rectangular parallelogram would be an isosceles trapezoid. Georgia guy (talk) 18:38, 18 March 2013 (UTC)
replies: text: Yes, see the comment above.  It's OK if you define "legs" as non-parallel sides, but then the set of rectangles would not be a subset of the isosceles trapezoids.  The recent change by David Eppstein sorts out the problem.  Dbfirs 22:50, 18 March 2013 (UTC)
thread_title:  Bad definition 

message: I gather from the previous discussions on this talk page that isosceles trapezoids must be defined to exclude non-rectangular parallelograms. Currently this article's lead says
:In Euclidean geometry, an isosceles trapezoid (isosceles trapezium in British English) is a convex quadrilateral with a line of symmetry bisecting one pair of opposite sides. 
Not sure, but it seems that this permits parallelograms. The article Symmetry (geometry) says
:Under an isometric transformation, a geometric object is said to be symmetric if, after transformation, the object is indistinguishable from the object before the transformation, i.e., if the transformed object is congruent to the original.[5]
Doesn't either of the (bimedian) lines bisecting two opposite sides of a parallelogram cut it into congruent pieces? Then the parallelogram is symmetric, and each bimedian is a line of symmetry, so the article's current definition includes parallelograms. 
Maybe this could be fixed by changing "line of symmetry" in our definition to "line of reflectional symmetry"? Loraof (talk) 17:34, 9 April 2016 (UTC)
replies: text: A parallelogram that is neither a rectangle nor a rhombus has no lines of symmetry. A line of symmetry (in 2 dimensions) means reflection symmetry. Rotational symmetry is defined by a point, not a line, unless we're dealing with 3-dimensional figures. Georgia guy (talk) 17:43, 9 April 2016 (UTC)
replies: text: Right, our redirect Line of symmetry reflects (ahem) what you say. Loraof (talk) 21:59, 9 April 2016 (UTC)

text: What's the difference between "equal to" and "congruent to"? Loraof (talk) 19:32, 11 April 2016 (UTC)
replies: text: Congruence is precisely defined in Mathematics (see Congruence (geometry), though I expect you already know the definition).  "Equal to" is not clearly defined for shapes because one needs to specify which properties are equal.  I've removed the misleading "equal to" in the article, and also the misleading reference to congruence.  Dbfirs 20:58, 11 April 2016 (UTC)
thread_title:  Parallelograms again 

message: The reference in question excludes rectangles only in that it uses the exclusive definition of trapezoid - rectangles are being excluded because the text does not consider them trapezoids at all (much less isosceles trapezoids). Since Trapezoid defaults to the inclusive definition, I'd assume we'd want to maintain that here. If we want to note that an exclusive definition of isosceles trapezoid excludes rectangles, then we should say that explicitly. It is unclear if that was the intended meaning here, or if this also refers to other definitions that exclude rectangles for whatever reason (in which case, we need citations of those).66.211.251.59 (talk) 19:35, 7 July 2022 (UTC)
thread_title:  Citation 2 (Referenced under "Special Cases") is inappropriate.