(1) synthesis method (cause and effect), starting from known conditions, through the application of relevant definitions, theorems and axioms, gradually advances until the problem is solved;
(2) Analysis method (fruit-seeking method) considers the conclusion of the proposition, considers the conditions needed to establish it, and then continues to consider the required conditions as the conclusion to be proved, and so on until the facts are known;
(3) Double-headed method: combining analysis with synthesis. Comparatively speaking, analytical method is conducive to thinking, and comprehensive method is easy to express. Therefore, when thinking about problems in practice, we can combine them and deal with them flexibly, so as to shorten the distance between the topic and the conclusion and finally achieve the purpose of proof.
There are two basic types of geometric proofs:
First, the quantitative relationship of plane graphics;
The second is about the positional relationship of plane graphics.
These two kinds of problems can often be transformed into each other, for example, proving parallel relations can be transformed into proving equal angles or complementary angles.
For example, there can be such a thinking process: prove that two sides are equal, as can be seen from the picture, we only need to prove that two triangles are equal; Prove triangle congruence, and combine the given conditions to see what conditions need to be proved and how to make auxiliary lines to prove this condition.
Refer to the above content: Baidu Encyclopedia-Geometric Proof