Date: Sat, 17 Oct 1998 10:49:45 EDT
Subject: Supplimentary and Complimentary Angles

I am in 9th grade and my math teacher wanted us to find out why complimentary angles are called complimentary and why supplimentary angles are called supplimentary. I have looked everywhere and asked numerous people, but I have yet to find an answer. My math teacher said it had something to do with trigonometry. Do you have an answer for me?

Thank You,

Hi Christina
Looking up the words in a good dictionary will probably lead you in the correct direction but you have to spell the words correctly. The English words complement and compliment have quite different meanings, although at one time there was one spelling, with the e, for both meanings. I asked a Greek friend what is used in Greek as many of the words we use in geometry have a Greek origin. He said that the words are essentially the same in Greek as they are in English.
  Early studies of angles and triangles most often involved right angled triangles. In particular given an angle it was important to know what other angle was needed to complete a right angled triangle, that is, what was its complement. On the other hand the supplement doesen't complete the triangle but adds to it as you might supplement your diet with vitamins. The earliest reference we found to the phrase supplementary angle was a reference to a 1796 mathematics dictionary which says "The complement to 180 degrees is uaually called the supplement."

Chris and Penny

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