Euclides proves proposition 6 in book I using a reductio ad absurdum proof assuming that line AB is less than line AC.
Couldn't we just draw a circle with center A and distance B, and by definition 15 prove that AB = AC, as described in the following figure?
You can see the proposition in this link http://aleph0.clarku.edu/~djoyce/java/elements/bookI/propI6.htm.