# confusion about ‘median’

For a triangle, ‘median’ and ‘midsegment’ are two different things, the former defined in Wikipedia’s article ‘Median (geometry)’, and the latter defined in Wikipedia’s article ‘Medial triangle’. (Note that Wikipedia’s article ‘Median (geometry)’ is distinct from Wikipedia’s article ‘Geometric median’.) The confusion that we want to highlight here is that for a trapezoid, the triangle meaning of ‘median’ is not of interest and not used, but the idea of ‘midsegment’ is of interest and used, but is usually labeled with the term ‘median’ (and only occasionally labeled with the term ‘midsegment’). Such usage occurs in the nuts-and-bolts realm of mathematics homework problems and mathematics tournament problems, and so the students need to be on their toes as to this ambiguity that is not at all addressed on Wikipedia’s disambiguation page for ‘median’. It is true that in Wikipedia’s article on trapezoids the term ‘midsegment’ is used, with a parenthetical note of ‘median’ being an alternative term, but this is opposite of popular usage (the popular usage being the one given by Merriam-Webster in its free online dictionary).
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