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### Complementary and Supplementary Angles

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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
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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/
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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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Associated Topics:
High School Definitions
High School Euclidean/Plane Geometry
High School Geometry
Middle School Definitions
Middle School Geometry
Middle School Two-Dimensional Geometry

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