The key is to be familiar with theorems and the like, and to use them skillfully. Some questions can be combined with several questions. Half of the proof questions that need auxiliary lines are intercepted on the long ones or extended on the short ones. You must never walk into a dead end.

Remember the definition accurately and use it flexibly.

It can be defined by reduction to absurdity (a common practice of mathematical proof): the method of proving a theorem first puts forward a hypothesis that is contrary to the conclusion in the theorem, and then draws a result that is contradictory to the known conditions from this hypothesis, thus denying the original hypothesis and affirming the theorem. Also called reduction to absurdity. The reduction to absurdity is actually to prove that the negative proposition of a proposition is correct, which is equivalent to direct proof, but it may be easier to prove its negative proposition. The above contradiction is actually the conclusion that the hypothesis is incompatible with the topic, so we can't accept this hypothesis, so the opposite of this hypothesis is correct, so the proposition is proved. Scope of application: To prove some propositions, it is difficult to prove them positively, and the situation is more or more complicated, while the opposite is relatively simple. Prove that there are infinitely many prime numbers. This ancient proposition was originally given by the ancient Greek mathematician Euclid (living in Alexandria, about 330-275 BC, the most famous mathematician in ancient Greece) in his immortal book Elements of Geometry: If the proposition is not established, there are only a limited number of prime numbers, and all prime numbers are 2 = A 1