There is always a shadow of geometric proof questions in the mathematics test paper of senior high school entrance examination, but geometric proof questions often make our thinking stuck, which not only delays a lot of time to solve problems, but also affects the rhythm and mood of answering questions. So what skills do we have in the face of geometric proof? Teacher Doudou shared an example with you today.

Today's example

Thinking analysis

It is required to prove that the two angles are equal, but we find that there is no direct connection between the two angles through observation, so how to construct the connection between them?

At this time, we found through inspection that M and N are the midpoint of AB and CD respectively. As a big math problem, it will definitely not tell us useless information. Then we have to think about which knowledge points can use the midpoint. At this time, we have to think in our minds: the center line. Using the characteristics of the midline (the midline of a triangle is parallel and equal to half of the base), the relationship between angles is constructed, and finally the answer we want to prove is obtained.

Detailed answer

Summarize and consolidate

Through this example, we can find that when we see the information about the midpoint in the question, we have to establish the connection between different angles by adding auxiliary lines to construct the midline. Therefore, when we see the topic, we should not rush to write, first analyze the structure of the picture in the topic, and at the same time highlight special circumstances (such as midpoint, angular bisector, vertical line and so on). ) tell us in the topic, then spread our ideas in our minds, recall the knowledge points related to this information, and finally start solving problems.

Ok, that's all for today's sharing. If so, please pay attention to forwarding support. Your little effort is the greatest help to me!