In my country, for many years, trapezoid is defined as such in the textbooks:

a quadrilateral with only two parallel sides.

But today, referring to foreign sources, someone told me that:

a quadrilateral with at least two parallel sides.

Wikipedia uses a similar definition. I want to know that does it make sense for a trapezoid to have more than one pair of parallel sides? Does it make sense for a quadrilateral to have for example, three parallel sides? What's wrong with the former definition?

  • $\begingroup$ Your country's definition is not correct. $\endgroup$ – user230734 Aug 15 '15 at 22:52
  • 3
    $\begingroup$ Inclusive definitions tend to be more advantageous. If I have a quadrilateral with a pair of parallel sides, I may not care what's going on with the other pair of sides. If they aren't parallel, fine; if they are, that's okay, too. With your first definition, I'd have to describe my quadrilateral as "a trapezoid-or-parallelogram", which would be tedious, while also calling too much attention to the sides that don't interest me. Allowing parallelograms to be special cases of trapezoids (just as squares are special cases of rectangles) simplifies discussion. $\endgroup$ – Blue Aug 15 '15 at 22:53
  • $\begingroup$ Almost everything that's true about trapezoids is also true about parallelograms. $\endgroup$ – Akiva Weinberger Aug 16 '15 at 2:23

There is nothing wrong with thinking of a trapezoid as having only one pair of parallel sides but the official definition would be that it is "a convex quadrilateral with at least one pair of parallel sides"(as written in the wikipedia page). The idea is that if a trapezoid has two pairs of parallel sides then it is still a trapezoid but also a parallelogram in addition to being a trapezoid. So all parallelograms are trapezoids and you could think of it as there is a type of trapezoid that has two pairs of parallel sides and the more intuitive type which has only one pair of parallel sides.


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