How to prove theorems?

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How to prove theorems?

The procedure of proving a theorem only seems complicated. It is enough to be able to think logically, to have the necessary knowledge of this scientific discipline, and it will not be difficult for you to prove the theorem. It is important to carry out all actions clearly in the correct sequence.

In some sciences, for example, in algebra and geometry, one of the most important skills is the ability to prove theorems. This is due to the fact that the theorems proved later will be useful in order to solve problems. It is necessary not only to learn the algorithm of the proof, but to be able to understand its essence. Let's see how to prove theorems.

Proof of Theorems

First you need to make a drawing, it must be clear and accurate. After that you need to note on it the specified conditions. In the column "Dano" you need to write down all the values ​​that you originally knew, and what you need to prove. After that, you can do proof. In essence, this is a chain of logical thoughts that allow us to show that a statement is true.The proof of the theorem implies the use of other theorems, axioms, the application of an action by contradiction, etc.

So, the proof of the theorem is a certain sequence of actions that allow one to obtain a statement whose truth cannot be disputed. As a rule, the most difficult thing during the proof is just the search for a sequence of logical reasoning. If this succeeds, then you can prove what was required of you.

How to prove theorems on geometry without difficulty

To simplify your task, you can break the theorem into parts, and prove each of them separately, which ultimately leads you to the result. In some cases, effectively using the method of "proof by contradiction." Then you need to start with the words "suppose the opposite." It should be explained why in this case this or that conclusion is impossible. It is necessary to finish with the words “it means that the initial statement is true. The theorem is proved.


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