Math Is Fun Forum

Al-Allo

Member

Registered: 2012-08-23

Posts: 324

Euclid's elements proposition 17. The sum of two angles in a triangle

I have a very short question on this proposition : http://aleph0.clarku.edu/~djoyce/java/elements/bookI/propI17.html

I understand the way the theorem was proved. Euclid proves that angles ABC and ACB is less than 180 degrees. At the end, he says the same method can be applied to prove for the other cases. I was able to do the same for the angle BAC and ACB. But how do I do it for CAB and ABC ? It doesn't seem the same method holds for this case, am I right ?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,143

Re: Euclid's elements proposition 17. The sum of two angles in a triangle

Have you looked back to prop 16 ?  Why cannot you just turn the triangle to  bring a fresh angle into the required position, re-lettering the points as required?

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob