Two-column proofs are a little foreign to most of us - even to mathematicians, who don't usually use such a rigid way of writing a proof once they have learned what it means to prove something.
It's really more like writing an essay than like the math you've done before now - more creative and less mechanical. That makes it harder, but also more rewarding and even fun.
For in-depth discussions of proof, see Preuve-Proof-Prueba, the international newsletter on the teaching and learning of mathematical proof. We also recommend highly "Proofs Without Words the "Pythagorean Theorem" (with over 20 proofs and "Proofs in Mathematics a discussion of the value of proofs in the classroom followed by a collection of proofs classified as "simple" or "charming all three articles.
A proof is just an orderly way to show that something is true, by building on other things you know are true. The only way that order matters is that each thing you say must be based on something you've already said.
The first is to understand and be aware of the definitions of each of the terms associated with what you are trying to prove. Second, know and understand previous proven theorems related to what you are trying to prove.
Your "givens" are the foundation someone laid for you, and the theorems you have are the girders and rivets you have to put together to make the tower. Let's try drawing your sample proof as a building, to show how its parts are connected.
- Doctor Pete, learning, proofs, i'm interested in learning how to do proofs. Can you recommend some good books on the different techniques used and how they are applied? What a proof is depends on whether you are talking about math, science, law, politics, etc.