Geometric Proofs: Is the Point Obvious?

This process trains the mind to think logically and critically. In summary, geometric proofs serve as a systematic process to understand geometric relationships and develop logical and critical thinking skills.
  • #1
Stratosphere
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Is there a point to geometric proofs? The ones that I have encountered are so obvious that it almost seems useless to have to use them for anything.
 
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  • #2
I always hated the ones that we had to do in high school geometry class. They destroy everything enjoyable about solving a geometric problem by reducing it to a systematic process. If you don't like them don't let it turn you off from geometry or proofs in general.
 
  • #3
Stratosphere said:
Is there a point to geometric proofs? The ones that I have encountered are so obvious that it almost seems useless to have to use them for anything.

The purpose of Geometric proofs is to understand the truth or falsity of a Geometric relationship or Geometric statement. Performing easy proofs develops your ability to do proofs which enables you enough intellectual conditioning and content knowledge to perform more difficult proofs.
 

1. What is a geometric proof?

A geometric proof is a logical argument that uses mathematical principles and properties to show that a statement or theorem is true. It typically involves a series of steps, starting from given information and using deductive reasoning to arrive at a conclusion.

2. How do you know if a point is obvious in a geometric proof?

In a geometric proof, a point is considered obvious if it can be easily identified or inferred from the given information and the previously established statements. It should not require any additional assumptions or complicated reasoning to understand why the point is true.

3. What is the difference between an obvious point and an assumed point in a geometric proof?

An obvious point is one that can be easily identified or inferred from the given information and the previously established statements. It does not require any additional assumptions or complicated reasoning to understand why the point is true. On the other hand, an assumed point is one that is not explicitly stated or given, but is necessary to make the proof work. It requires an additional assumption or reasoning to understand why the point is true.

4. How do you prove that a point is obvious in a geometric proof?

To prove that a point is obvious in a geometric proof, you need to provide a clear and concise explanation that shows why the point can be easily identified or inferred from the given information and the previously established statements. This can be done by using logical reasoning, mathematical principles, and properties to support your explanation.

5. Can a point be considered obvious in a geometric proof if it is not explicitly stated or given?

Yes, a point can be considered obvious in a geometric proof even if it is not explicitly stated or given. As long as the point can be easily identified or inferred from the given information and the previously established statements, it can be considered obvious. However, it is important to provide a clear explanation to support why the point is obvious in the proof.

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