I started to study the axioms of Euclidean Geometry and i wanted to prove by myself a theorem (using only the axioms and rules of Euclidean Geometry):
For 3 non-aligned points passes a unique plane.
However, I don't know how to do it. Can you help me?
ps: I found the previous statement (which i called "theorem) called "corollary". To me theorems and corollaries seems the same thing. Am I wrong ?
The theorem is provable by the rules and principles of Euclidean geometry. In fact Euclid seems to prove it in Elements, XI, 1 (his first theorem in the three books of solid geometry: "A part of a triangles does not lie in one plane and a part in a plane more elevated", i.e. in a different plane. If three non-aligned points determine a triangle, and XI, 1 proves that every triangle is in one plane only, then it seems the theorem follows from Euclidean principles, or at least Euclid thought it did. The theorem seems so nearly self-evident that some have wondered whether the short reductio proof he offers is really doing any work.