Mathematics knowledge points from grade one to grade three
1, there is only one straight line between two points.
2. The line segment between two points is the shortest.
3. The complementary angles of the same angle or equal angle are equal.
4. The complementary angles of the same angle or equal angle are equal.
5. There is one and only one straight line perpendicular to the known straight line.
6. Of all the line segments connecting a point outside the straight line with points on the straight line, the vertical line segment is the shortest.
7. The parallel axiom passes through a point outside the straight line, and there is only one straight line parallel to this straight line.
8. If two straight lines are parallel to the third straight line, the two straight lines are also parallel to each other.
9. The same angle is equal, and two straight lines are parallel.
10, internal dislocation angles are equal, and two straight lines are parallel.
1 1, the inner angles on the same side are complementary, and the two straight lines are parallel.
12, two straight lines are parallel and have the same angle.
13, two straight lines are parallel and the internal dislocation angles are equal.
14. Two straight lines are parallel and complementary.
15, the sum of two sides of a theorem triangle is greater than the third side.
16, the difference between two sides of the inference triangle is smaller than the third side.
17, the sum of the internal angles of the triangle and the theorem triangle is equal to 180?
18, it is inferred that the two acute angles of 1 right triangle are complementary.
19, Inference 2 An outer angle of a triangle is equal to the sum of two inner angles that are not adjacent to it.
20. Inference 3 The outer angle of a triangle is larger than any inner angle that is not adjacent to it.
2 1, the corresponding edge of congruent triangles is equal to the corresponding angle.
22. The edge axiom (SAS) has two edges, and their included angle corresponds to the congruence of two triangles.
23. The corner axiom (ASA) has two corners and two triangles with equal corresponding sides.
24. Inference (AAS) has two angles, and the opposite side of one angle corresponds to the congruence of two triangles.
25. The side-by-side axiom (SSS) has the congruence of two triangles whose three sides correspond to each other.
26. Axiom of hypotenuse and right-angled side (HL) Two right-angled triangles with hypotenuse and a right-angled side are congruent.
27. Theorem 1 The distance from the point on the bisector of the angle to both sides of the angle is equal.
28. Theorem 2 The point where two sides of an angle are equidistant is on the bisector of this angle.
29. The bisector of an angle is the set of all points with equal distance to both sides of the angle.
30, the nature theorem of isosceles triangle The two bottom angles of an isosceles triangle are equal (that is, equilateral angles)
3 1, inference 1 The bisector of the vertex of the isosceles triangle bisects the base and is perpendicular to the base.
32. The bisector of the top angle, the median line on the bottom edge and the height on the bottom edge of the isosceles triangle coincide with each other.
33. Inference 3 All angles of an equilateral triangle are equal, and each angle is equal to 60?
34. Decision theorem of isosceles triangle If a triangle has two equal angles, then the sides of the two angles are also equal (equal angles and equal sides).
35. Inference 1 A triangle with three equal angles is an equilateral triangle.
36. Inference 2 has an angle equal to 60? An isosceles triangle is an equilateral triangle.
37. In a right triangle, if an acute angle equals 30? Then the right-angled side it faces is equal to half of the hypotenuse.
38. The midline of the hypotenuse of a right triangle is equal to half of the hypotenuse.
39. Theorem The point on the vertical line of a line segment is equal to the distance between the two endpoints of this line segment.
40. The inverse theorem and the equidistant point between the two endpoints of a line segment are on the vertical line of this line segment.
4 1, the middle vertical line of a line segment can be regarded as the set of all points with equal distance at both ends of the line segment.
42. Theorem 1 Two graphs symmetric about a straight line are conformal.
43. Theorem 2 If two figures are symmetrical about a straight line, then the symmetry axis is the perpendicular line connecting the corresponding points.
44. Theorem 3 Two figures are symmetrical about a straight line. If their corresponding line segments or extension lines intersect, then the intersection point is on the axis of symmetry.
45. Inverse Theorem If the straight line connecting the corresponding points of two graphs is vertically bisected by the same straight line, then the two graphs are symmetrical about this straight line.
Junior high school mathematics learning methods
First, preview before class
Pre-class preparation is neglected by many students and parents, who prefer to spend a lot of time in remedial classes. In fact, prepare well before class on time, so that you can focus on the class. Focus on what you don't understand in class and take notes. Review in time after class. Learning is a step-by-step process, and you won't eat a fat man in one bite; Instead of biting off more than one can chew, it is better to follow the normal learning rules, which will neither delay learning nor play.
Second, lay a good foundation in mathematics.
In mathematics learning, mathematical concepts, definitions of basic theorems and formulas are the basis. Students must first understand, learn to verify when they need to verify, and deduce whatever they can; Only in this way can we understand memory; Really learn. If you don't understand the basic concepts, theorem definitions and formulas, you can't remember them; How do you do this problem? Therefore, laying a good foundation is the key.
Third, be familiar with the examples and thoroughly understand the textbooks.
Mathematics examination and senior high school entrance examination are based on textbooks. So the examples in the book must be thoroughly understood. Go through all the knowledge points in the textbook; Key memory.
Fourth, do the questions in time after class.
Practice after class, and do it in time after learning a lesson. Consolidate what you have learned; Ask the teacher or classmates in time if you don't understand.
Fifth, do synchronous training questions.
The application of mathematical formulas and theorems also needs to do some synchronous training questions in peacetime. But not greedy. You must learn and understand what you do. Summarize other people's methods, find out the gaps and make up for the shortcomings.
Sixth, summarize more comparative memories.
There are many similar or similar theorem definitions and formulas in mathematics. We should be good at summing up their differences and connections. For quick memory. Doing problems is also to sum up good problem-solving methods and skills; It will take a step forward.
Introduction to junior high school mathematics learning
1. Students are often not good at reading math books, and in the process of reading, they often follow the method of rote learning. So how to read math books effectively? Usually should do:
One is rough reading. First, browse the branches of the textbook and grasp the general situation, key points and difficulties of this chapter;
The second is to read carefully. Read, experience and think about important concepts, properties, judgments, formulas, laws and ways of thinking repeatedly, understand their essence and causality, and mark out what you don't understand (for reference);
The third is learning. It is necessary to study the internal relationship between knowledge, explore the intention of book knowledge arrangement, and analyze, summarize and summarize knowledge in order to form a knowledge system and improve the cognitive structure.
Reading, first seek to understand, and then seek to read thoroughly, so that self-study ability and practical application ability can be well exercised.
2. The method of listening. ? Listen. It is to accept knowledge directly with the senses, but junior high school students often can't adapt to the increase of courses and classroom learning, can't see one thing clearly, lose energy, and reduce the effect of listening to lectures. Therefore, we should pay attention to the following points when listening to the course:
(1) Listen to the learning requirements of each class;
(2) Listen to the introduction and formation of knowledge;
(3) Understand the important and difficult points in teaching (especially the knowledge points that are not understood or questioned in the preview);
(4) Listen to the tips of the key part of the example and apply the mathematical thinking method;
(5) Make a summary after class.
3. Way of thinking. ? Think? Refers to the thinking of classmates. Mathematics is the gymnastics of thinking, learning can not be separated from thinking, and mathematics can not be separated from thinking activities. If you are good at thinking, you can learn vividly and efficiently. If you are not good at thinking, you will learn to die and the effect is poor. It can be seen that scientific thinking method is the premise of mastering knowledge. The thinking of seventh-grade students often stays in the thinking of primary schools and is narrow-minded. Therefore, in learning to do:
(1) Dare to think, be diligent in thinking, read and think, and listen and think. See more, listen more and practice more;
(2) Good at thinking. Will grasp the key of the problem and the focus of knowledge to think;
(3) reflection. We should be good at analyzing, summarizing and summarizing the advantages and disadvantages of problem-solving strategies and methods.
4. the method of asking. Confucius said:? Sensitive and eager to learn, not ashamed to ask questions. ? Einstein said: It is more important to ask questions than to solve them. ? Asking can solve doubts, asking can know new things, and learning in any subject begins with questions. Therefore, students should master some questioning methods in their usual study, mainly including:
(1) Question mode. That is, after answering a question, follow the train of thought to chase the question and continue to ask questions;
(2) rhetorical questions. Ask questions in the opposite direction according to the textbook and what the teacher said;
(3) Analogy to questioning method. According to the relationship between some similar concepts, theorems and properties, questions are raised through comparison and analogy.
(4) Contact the actual way of asking questions. Combined with some knowledge points, through the observation and analysis of some phenomena in real life, some problems are put forward.
In addition, when asking questions, you should not only ask why, but also ask why.
5. The method of taking notes. A large number of students think that mathematics does not take notes, and it is unreasonable for students who take notes to take notes. Usually what the teacher writes on the blackboard is written down. Remember? Instead? Listen. And then what? Think? . Although some notes are well written, they are of little use. Therefore, students should do the following when taking notes:
(1) in? Listen. ,? Think? Selectively recorded in;
(2) Remember the main points of the learning content, remember your own doubts, and remember the knowledge that is not in the book and the knowledge points added by the teacher;
(3) Remember the ideas and methods of solving problems;
(4) Remember the class summary. Clear notes are for supplement? Listen. Disadvantages are prepared for final review, and good notes can make review twice the result with half the effort.
Correct learning attitude and scientific learning methods are the two cornerstones of learning mathematics well. The formation of these two cornerstones can not be separated from the usual mathematics learning practice. So it is necessary to set aside some time for yourself to study math every day during the summer vacation.
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