In fact, there are some skills and methods to solve this kind of problem. In the process of solving problems, we can start with the following points.
Have you mastered the basic knowledge of 1? Will I use it flexibly?
There is a misunderstanding about knowledge mastery. Mastery here is not memorizing formulas and definitions, but thorough understanding. Many of them will "invent" some theorems Although we encourage innovation, we should not go too far. Mathematics pays attention to logic.
Only by thoroughly understanding the knowledge points can we see through the questions at a glance. Then you have a direction to answer.
For example:
This topic is called daily vol.8 example. To get this topic, we must first lock the scope.
How to find it?
The first problem is to verify AB+AC > 2AD. Does it feel familiar? That's right, it's a triangle.
"The sum of any two sides of a triangle is greater than the third side."
It can be seen that being familiar with knowledge points will bring you the right direction to solve problems.
Read the questions carefully.
Including three points: ① be cautious; ② Mark important conditions; (3) remember the topic.
Needless to say, be careful.
What are the important conditions? When reading the question, you should mark every condition in the given graph, such as "D is the midpoint on the side of BC" given in the above question.
Well, about the midpoint, there are four common methods to solve the problem in junior high school: three lines in one, right triangle hypotenuse midline, midline and double length midline method.
Then let's analyze it.
The combination of three lines is used for isosceles triangle or equilateral triangle. This problem has no obvious characteristics, so rule it out.
The center line of hypotenuse of right triangle is used for right triangle, which has no obvious characteristics and is excluded.
The midline is connected by the midpoint of both sides. This problem has no obvious characteristics, so rule it out.
Finally, the double long midline method is the key to solve the problem! ! !
Use this method to make auxiliary lines, and then deduce.
What is remembering a topic?
A topic is usually read more than twice. Preview the general questions for the first time, mark the known conditions in the diagram for the second time, and find the key points for the third time. Only by completing this process can you keep the topic in mind, put a question mark in your mind and find out the corresponding knowledge points.
It can be seen that careful examination of the questions will bring you clear ideas for solving problems.
3 cultivate methods to solve problems
There are many ways to solve problems, and not all of them can be explained clearly in one or two articles. Let me give you an example.
Inverse deduction is also the most common method in geometric proof.
In fact, when this article illustrates this topic, it is subtly telling everyone how to use the reverse method. Please see:
The first problem is to verify AB+AC > 2AD. Does it feel familiar? That's right, it's a triangle. "The sum of any two sides of a triangle is greater than the third side."
In fact, starting from the problem, after clarifying the trilateral relationship of the triangle, you will find the corresponding triangle. If the topic does not directly give the side length related to the conclusion, obviously you need to build such a triangle as an auxiliary line, and the idea naturally shifts to the drawing solution with the "double-length midline method".
Yes, it's as simple as that. Of course, you don't have to learn one topic to know all the topics. Mathematics has a routine, but it is not static, which requires students to use it flexibly.
It can be seen that cultivating correct problem-solving methods can smoothly sort out the reasoning process.
4 learn to reflect
Finally,
After mastering N kinds of problem-solving methods, students should also learn to reflect.
Every time after class, everyone will sum up, and they will sum up themselves, instead of me helping you.
Remember, I'm not helping you.
Reflect on what?
Reflect on the ways to solve problems, the ideas to solve problems, whether there are similarities in the problems done in the past, and the reasons why you can't solve them yourself.
Ask more why, the "why" you understand today is a shortcut to solve problems in the future.