{"id":165,"date":"2017-08-29T16:52:40","date_gmt":"2017-08-29T23:52:40","guid":{"rendered":"http:\/\/theothermath.com\/?p=165"},"modified":"2019-03-21T17:44:51","modified_gmt":"2019-03-22T00:44:51","slug":"what-is-a-trapezoid","status":"publish","type":"post","link":"https:\/\/theothermath.com\/index.php\/2017\/08\/29\/what-is-a-trapezoid\/","title":{"rendered":"What is a Trapezoid?"},"content":{"rendered":"

A famous bard once said, \u201cA trapezoid by any other name would still be a trapezium\u201d.<\/span><\/p>\n

Okay…totally not true. But it brings to mind the question I am often asked, \u201cWhat is the definition of a trapezoid?\u201d In fact, I was asked this question today. So here is my answer\u2026<\/span><\/p>\n

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For mathematics, being a subject that is supposedly the \u201cuniversal language\u201d, this question opens a huge can of worms and has a surprisingly involved answer.<\/span><\/p>\n

There are three \u2013 yes three \u2013 different ways one can define a trapezoid. Let\u2019s get started.<\/span><\/p>\n

If a person walks up to you and says, \u201cLet\u2019s discuss trapezoids\u201d, the first things you should do is listen his accent. Is it American? Is it Canadian? Or some other English-speaking accent? This matters.<\/span><\/p>\n

For the words trapezoid<\/span> and trapezium<\/span>, America and Canada defines them one way, but in other English speaking countries these same two words have their meanings switched.<\/p>\n\n\n\n\n\n
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In America and Canada…<\/span><\/p>\n<\/td>\n<\/tr>\n

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trapezium<\/span><\/p>\n<\/td>\n

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trapezoid<\/span><\/p>\n<\/td>\n<\/tr>\n

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\"\"<\/span><\/p>\n<\/td>\n

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\"\"<\/span><\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

 <\/p>\n\n\n\n\n\n
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In other English speaking countries…<\/span><\/p>\n<\/td>\n<\/tr>\n

\n

trapezium<\/span><\/p>\n<\/td>\n

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trapezoid<\/span><\/p>\n<\/td>\n<\/tr>\n

\n

\"\"<\/span><\/p>\n<\/td>\n

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\"\"<\/span><\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

\u00a0In America a trapezium is a quadrilateral that has no parallel sides. Sometimes this is called an irregular quadrilateral.<\/span><\/p>\n

\u00a0So now that we have define a trapezoid to be the figure that is not a trapezium. There is still the matter of the two definitions of trapezoid<\/span> in America.<\/span><\/p>\n

\u00a0Let\u2019s start with this figure\u2026<\/span><\/p>\n

\"\"<\/span><\/p>\n

\u00a0Most people would immediately recognize it as a trapezoid. There are two ways we can classify as trapezoid: the inclusive definition and the exclusive definition.<\/span><\/p>\n