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