Complementary and Supplementary Angles
Date: 09/30/98 at 19:49:49 From: Christina Saunders Subject: Why are angles called complementary or supplementary? My math teacher asked us to find out why angles are called complementary or supplementary, and not simply because they equal 90 degrees or 180 degrees. Please help! Thanks.
Date: 10/01/98 at 09:27:57 From: Doctor Peterson Subject: Re: Why are angles called complementary or supplementary? Hi, Christina. I can give you an answer, but it may not quite satisfy you. The word "complement" is related to the word "complete," and comes from a Latin word "complere" meaning "fill entirely." "Plere" in Latin means fill, and "com" is an intensive prefix, meaning "do it all the way." My dictionary says a "complement" is "something that completes, makes up a whole, or brings to perfection." A complementary angle "completes" a right angle (90 degrees). The word "supplement" is related to "supply," and comes from a Latin word "supplere" meaning "fill up"; "sub" means "from below." My dictionary says a supplement is "something added to complete a thing, make up for a deficiency, or extend or strengthen the whole." A supplementary angle "fills up" a straight angle (180 degrees). You'll notice there doesn't seem to be any particular reason to use one for 90 degrees and the other for 180 degrees. The two words are very nearly synonyms, both meaning "to fill up what's missing," without saying what the "whole" is that is being filled. In math we often need to invent special words with very precise meanings, and rather than make up entirely new words, we just give an existing word that special meaning. I suspect that one of these two words was used first, and then when the need for a word with the other meaning was recognized, they just looked for a different word that had a similar meaning and used that. There's not necessarily any specific reason to choose one or the other. I tried to find out the history of these words, but found nothing. Most likely they were first defined in Latin by medieval mathematicians, perhaps in translating Euclid, but I don't know for sure. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/
Date: 10/01/98 at 20:15:26 From: Anonymous Subject: Thank You! I just wanted to thank you for helping me with my problem. My next math class is tomorrow, so I'll see what my teacher says, but thanks a lot! Christina
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