Proving Geometry: Examples and Tips

[Dagenais]

In this book I am reading about Geometry, it is teaching on how to prove things.

It gives a bunch of examples that don't make much sense to me.

It has the picture, statement and the givens...then the Proof (what the writer is proving).

I am assuming that there was a theorem previous to this to prove, or do you have to chose something yourself to prove in Geometry?

 

[selfAdjoint]

I'll bet you are supposed to intuit the theorem in the process of working out the proofs. The book is not trying to teach you geometry but to teach you how creative mathematicians work.

 

[Dagenais]

I don't think so.

It gives a picture, and then the givens, and then the Proof Statement.

I was simply wondering when I start Geometry class, will I have to figure out what to prove myself, or will there be a theorem for me that I have to prove?

 

[Integral]

I am sure that you will start by proving a set of theorems based on the fundamental Axioms, then you will use those theorems to prove more involved theorems. The theorems you will be proving have been known for centuries, you will not have to come up with them on your own.

 

[Dagenais]

Okay, so basically they will ask me what to prove, and I won't have to find out myself, what I have to prove right?

I was looking at the book and it didn't make any sense, I could chose dozens of things to prove, I thought that their must be a Theorem that they give you to prove.

 

[Integral]

Be patient, there will be plenty of theorems to prove.

 

[HallsofIvy]

You said "It has the picture, statement and the givens".

The "statement" IS the theorem to be proven. The "givens" are a precise statement of the hypotheses of the theorem.