We have a preliminary knowledge about lines and started to explore shapes with more beautiful and complex characteristics. For triangles, on the one hand, we should study the properties of different elements (edges and angles) in a graph, on the other hand, we should pay attention to the relationship between two graphs. The congruence of two graphs is an important viewpoint in plane geometry, and it is also a powerful tool to prove the equality of line segments, angles and areas. So how to learn the proof of triangle congruence well? This requires diligent thinking, small steps forward, training from easy to difficult, and sublimation from imitation to independent reasoning, from reality (the topic has ready-made graphics) to nothingness (you need to draw your own graphics or add auxiliary lines). Specifically, it can be divided into three steps: the first step is to learn to solve simple problems with only one congruence, with the emphasis on imitation. During this period, we should pay attention to imitating the proof of textbook examples, so that our proof format is standardized, the language is accurate and the process is concise. If it is proved that two triangles are congruent, which two triangles must be written out, which is convenient for readers and lays the foundation for consciously looking for the needed congruent triangles in complex graphics in the future; At the same time, we should pay attention to the corresponding relationship of vertices to prevent corresponding errors; The three conditions required for completeness should be enclosed in braces; Every step should be full of reasons and train the rigor of thinking. After a period of training, you should be able to skillfully and independently prove the topic with clear direction and little change in content, and take a solid first step. The second step is to prove the two turning points and the final conclusion with congruence in a topic, and learn to analyze. When learning congruence between right triangle and isosceles triangle, gradually deepen the difficulty, learn to prove congruence twice in a topic, especially learn to find the proof method of topic in an orderly way by analytical method, which has strong purpose and clear thinking, and can effectively solve more complicated topics by combining comprehensive method. At the same time, there is generally more than one solution to the problem at this time. Efforts should be made to solve more than one problem, compare advantages and disadvantages, and sum up the laws. The third step is to learn proposition proof and master the commonly used method of adding auxiliary lines. The proof of proposition can fully temper the application ability of mathematical language (including graphic language), and the auxiliary line builds a bridge between the known and the unknown, which is difficult. Don't relax your efforts and give up all your previous efforts. At the same time, we should be familiar with some basic graphic properties, such as "angle bisector+perpendicular = congruent triangles". It is proved that congruence is nothing more than equidistant and angular conditions. So it is necessary to accumulate equidistant (or line segments, etc.) conditions. ), angle, etc. Existing or can be derived from normal study. Know it by heart, and it will be handy to use it.