Proving Geometry: Examples and Tips

In summary, the book is teaching the reader about Geometry and how to prove things. It provides examples and walks the reader through the process of proving theorems. The book assumes that the reader already knows the fundamental Axioms and will start by proving a set of theorems based on them. The reader will not have to come up with theorems on their own, as there are already known theorems that have been proven for centuries. The book also explains that the "statement" is the theorem to be proven and the "givens" are the hypotheses of the theorem.
  • #1
Dagenais
290
4
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?
 
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  • #2
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.
 
  • #3
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?
 
  • #4
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.
 
  • #5
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.
 
  • #6
Be patient, there will be plenty of theorems to prove.
 
  • #7
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.
 

1. What is the importance of proving geometry?

Proving geometry is important because it allows us to logically and mathematically justify the relationships and properties of geometric figures. By proving theorems and postulates, we can confidently use them to solve more complex problems and develop new theories.

2. How do I start a proof in geometry?

The first step in starting a proof is to identify what you are trying to prove. This can be a theorem, postulate, or a given statement. Then, use your knowledge of geometric properties and relationships to construct a logical argument using deductive reasoning.

3. What are some common proof techniques in geometry?

Some common proof techniques include using definitions and theorems, using algebraic manipulation, using geometric constructions, and using the properties of parallel and perpendicular lines. It is important to understand these techniques and when to apply them in a proof.

4. How can I check if my proof is correct?

To check if your proof is correct, you can follow these steps: 1) Read the given statement and the statements you have used in your proof, making sure they are all logically connected. 2) Check for any errors in your reasoning or calculations. 3) Make sure your conclusion logically follows from your statements. 4) Double check your work to ensure all steps are accounted for.

5. Can you provide some tips for writing a clear and concise proof?

To write a clear and concise proof, it is important to: 1) Use clear and concise language, avoiding unnecessary words or phrases. 2) Use correct notation and labeling to help organize your proof. 3) Justify each step with a reason, such as a definition or theorem. 4) Use diagrams or geometric constructions to aid in your explanation. 5) Double check your work for any errors or missing steps.

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