How to learn solid geometry well, how to learn solid geometry well?

Actually, geometry questions are relatively easy.

If you think about it, you start by learning a few theorems, such as the three-perpendicular theorem.

After memorizing, the questions will be smooth.

In addition, you need to increase your sense of space.

This requires an innate condition, and of course acquired efforts are also very important.

I think the key is to get the definition in the book clear and thorough.

Do more questions, but don't do those difficult questions, which are generally mid-range and low-grade questions, rescued or improved after a period of time.

The key to learning three-dimensional geometry well is to have the ability to think abstractly in space, and the cultivation is a gradual process. Solid geometry is simply a stack of multiple planar geometries, and it will be helpful to analyze them one by one. In addition, if you are really good at other parts of mathematics as you said, this place can consider giving up and focusing on other knowledge points.

The cultivation process of abstract thinking is also the meaning of learning solid geometry in high school. It takes a long time and has poor results. Depending on your time, it's up to you to give up.

Look at the pictures more and exercise your spatial thinking skills.

Solid geometry.

1. Establish the concept of space and strengthen the ability of spatial thinking!

2. Solid foundation of plane geometry: because the solution of three-dimensional geometry problems is dealt with on the plane, the knowledge of plane geometry is mostly used.

3. To be able to turn three-dimensional problems into plane problems, there are experience and skills here, and you will experience it by doing more questions!

4. Firmly grasp the concepts, theorems, laws, and formulas of solid geometry, and be able to strengthen it in the process of problem solving!

The above points are for your reference!

This is expert advice:

There are two keys to learning solid geometry well:

1. Graphics: It is very important to learn not only to read pictures, but also to learn to draw, and to cultivate their spatial imagination ability through reading and drawing.

2. Language: Many students can think about the problem clearly, but when it falls on paper, they can't speak. A word to remember:

Geometric language is the most important thing to say with evidence and reason. In other words, don't say anything that doesn't have a basis, and don't say anything that doesn't conform to the theorem.

As for how to prove the problem of solid geometry, we can study it from the following two perspectives:

1. Classify all theorems in geometry: the classification according to the known conditions of the theorem is the property theorem, and the classification according to the conclusion of the theorem is the decision theorem.

For example, if two straight lines parallel to the same straight line are parallel, it can be regarded as either the property theorem of the parallel nature of two straight lines, or it can be regarded as it.

Cheng is a decision theorem in which two straight lines are parallel.

For example, if two planes are parallel and intersect the third plane at the same time, then their intersection lines are parallel. It is both a theorem of the nature of two planes that are parallel.

Again, two judgment theorems with parallel straight lines. In this way, we can find what we need, for example: we want to prove a straight line.

and perpendicular to the plane, the following theorem can be used:

1) The determination theorem that lines and planes are perpendicular.

2) Two parallel perpendicular to the same plane.

3) A straight line and two parallel planes are perpendicular at the same time.

2. Be clear about what you want to do

Be sure to know what you're going to do! Before proofing, you must design a good route, clarify the purpose of each step, learn to make bold assumptions, and reason carefully.

A lot of bai

The student's subconscious mind will make such an inference du::

1) My stereo zhi geometry is not.

Good->2) Because I don't have a good version of the DA's spatial imagination power->3) Good spatial imagination should be innate->

4) Therefore, I am not good at stereo geometry because I am naturally "stupider" than others in this regard ->5) Therefore, no matter how hard I try, it is in vain.

And many teachers can't teach the law, so that those children who have worked hard still can't make progress, so they believe in the above reasoning even more, and eventually it becomes a vicious circle.

In fact, as long as you master the right method, you can improve the problem-solving ability of three-dimensional geometry by using Li Zeyu's three tricks of translation-specialization-staring at the target.

Learn to create a sense of three-dimensionality.

Don't memorize theorems and properties mechanically.

Rely on three-dimensional sense to understand theorems and properties, and then seek solutions to problems.

Do more questions, and you must be proficient in the theorems and properties of various lines, and learn to summarize. Geometry is nothing more than equal, parallel, perpendicular, and so on.

Solid Geometry The three-dimensional space in your mind is important! In other words, you need to have a three-dimensional coordinate system or three-dimensional space in your mind.

This is the ability to think, and it varies from person to person, because I made a lot of dioramas when I was a child, and I was exposed to a lot of structural structures, so learning stereo geometry at that time was the same as playing. So if you don't have the accumulation of thinking when you are young, you can also cultivate.

First of all, it's a good idea to have a set of materials on hand to build a three-dimensional shape, which is now available everywhere and should be easy to buy. Don't think that this is a child's building block, in fact, the so-called theorem and inference of solid geometry and other words are far less direct than the actual position relationship between points, lines and surfaces, after all, this is the most intuitive feeling. Slowly cultivate your spatial thinking ability through physical construction, and once the three-dimensional space in your mind is formed, you will be able to solve many problems when you think about it.

Many people have no problem learning plane geometry, but learning solid geometry collapses. It is because flat geometry can give you the most intuitive feeling on paper, and three-dimensional geometry on paper needs to be constructed in your thinking, so it is important to cultivate spatial thinking ability.

In addition, in terms of problem-solving skills, in fact, I personally think that many solid geometries have actual skills that are far lower than those of plane geometry, whether it is graphic problem solving or vectors. So if you can decompose the solid geometry into planes (because a volume is a collection of faces, and when you dissolve a problem, you actually solve a multifaceted problem), it will be a lot easier, of course, all based on your spatial thinking, depending on how skilled you are.

It may be a mess, I hope it can help you.

You see, do you understand? If you don't have any words, I'll explain!

The most important thing here is the method, and if you master the method, similar problems can be solved!

Hope mine is helpful to you and good luck! Try more questions like this yourself, and you'll do it next time!

Good luck with your studies!

In fact, it is very simple, Stereo geometry may have a little headache when you first come into contact with it, and you can't figure it out, teach you a way, read the concept, read it every day, just get familiar with it, and understand! In fact, you can consult your teacher in this regard.