Talk:SSS postulate

I thought the SSS Postulate corresponded more to Proposition 4 in Book 1 of the Elements, not Proposition 8. Proposition 8 says that if the two legs and base of

I thought the SSS Postulate corresponded more to Proposition 4 in Book 1 of the Elements, not Proposition 8. Proposition 8 says that if the two legs and base of one triangle are equal to the two legs and base of another triangle, then the angle between the legs on both triangles would be the same. Mathwizard44 (talk) 14:18, 5 August 2009 (UTC)Reply

Proposition 8 is better

Latest comment: 11 years ago2 comments2 people in discussion

Proposition 4 from Elements is SAS. Proposition 8 states that, given equal respective sides, there is an equal angle as well, thereby reducing congruence to SAS (Proposition 4). My feeling is that Proposition 8 is a better reference for SSS since it has the SSS hypotheses, even though it doesn't immediately have the congruence conclusion. — Preceding unsigned comment added by 99.95.128.188 (talk) 02:48, 23 April 2014 (UTC)Reply

I decided to edit the page. While Euclid doesn't prove the two triangles to be "equal" in Prop. 8, it is still the proposition that first introduces this possibility. To any person reading the book it is obvious that Prop. 8 shows the same thing for three sides that Prop. 4 shows for two sides and the angle between them. Also, I would argue that since the terms "side" and "base" are arbitrary, you can manipulate your language to prove any two matching angles to be of equal size, making SSS and Prop. 8 functionally the same in a lot of cases. --Farco (talk) 22:02, 16 August 2015 (UTC)Reply

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