What are geometry proofs?

1 Answer
Nov 24, 2015

Proof is a sequence of logical statements, every subsequent one being a consequence of the previous, that leads to a statement that requires this proof.


What is important in this sequence is that it should start with a statement we consider to be true. It might be one or more axioms that we accept without any proof and consider true by definition and/or it might be one or more statements that were previously proven to be true.

Another important consideration is how we derive a logical statement from some preceding one. This derivation must be done according to rules of logic.

So, if we start with one or more true statements and derive some new statement using the rules of logic, our result is another true statement. To build a sequence of such derivations that leads to a statement that is required to be proven is the proof.