Knowledge is a treasure house, and practice is the key to it. Learning any subject requires not only a lot of memory, but also a lot of practice, so as to consolidate knowledge. Here are some eighth-grade math knowledge points I have compiled for you, hoping to help you.

The corresponding edge and the corresponding angle of congruent triangles are equal.

2. Angular Axiom (SAS) has two sides and two triangles with equal included angles.

3. Angle and Angle Axiom (ASA) has congruence of two triangles, which have two angles and their sides correspond to each other.

4. Inference (AAS) has two angles, and the opposite side of one angle corresponds to the congruence of two triangles.

5. The side-by-side axiom (SSS) has two triangles with equal sides.

6. Axiom of hypotenuse and right-angled edge (HL) Two right-angled triangles with hypotenuse and a right-angled edge are congruent.

7. Theorem 1 The distance between a point on the bisector of an angle and both sides of the angle is equal.

8. Theorem 2 The point where two sides of an angle are equidistant is on the bisector of this angle.

9. The bisector of an angle is the set of all points with equal distance to both sides of the angle.

10, the property theorem of isosceles triangle, the two base angles of isosceles triangle are equal (that is, equilateral angles)

1 1, it is inferred that the bisector of the vertices of 1 isosceles triangle bisects the base and is perpendicular to the base.

12. 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.

13, inference 3 All angles of an equilateral triangle are equal, and each angle is equal to 60.

14, the judgment theorem of isosceles triangle If a triangle has two equal angles, then the opposite sides of the two angles are also equal (equal angles and equal sides).

15, inference 1 A triangle with three equal angles is an equilateral triangle.

16, inference 2 An isosceles triangle with an angle equal to 60 is an equilateral triangle.

17. In a right-angled triangle, if an acute angle is equal to 30, the right-angled side it faces is equal to half of the hypotenuse.

18. The midline of the hypotenuse of a right triangle is equal to half of the hypotenuse.

19, it is proved that the distance between the point on the middle vertical line of a line segment and the two endpoints of the line segment is equal.

20. The inverse theorem and the point where the two endpoints of a line segment are equidistant are on the vertical line of this line segment.

2 1, the middle vertical line of a line segment can be regarded as the set of all points with the same distance at both ends of the line segment.

22. Theorem 1 Two graphs symmetric about a straight line are conformal.

23. Theorem 2 If two figures are symmetrical about a straight line, then the symmetry axis is the perpendicular line connecting the corresponding points.

24. Theorem 3 Two graphs 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.

25. 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.

26. Pythagorean Theorem The sum of squares of two right angles A and B of a right triangle is equal to the square of the hypotenuse C, that is, A 2+B 2 = C 2.

27. The Inverse Theorem of Pythagorean Theorem If the three sides of a triangle are related A 2+B 2 = C 2, then the triangle is a right triangle.

28. Theorem The sum of the internal angles of a quadrilateral is equal to 360 degrees.

29. The sum of the external angles of the quadrilateral is equal to 360.

30. Theorem The sum of the interior angles of a polygon is equal to (n-2) × 180.

The second volume of the second day summarizes the knowledge points of mathematics. Chapter 1: One-dimensional linear inequalities and one-dimensional linear inequalities.

First, the unequal relationship.

1, the formula connected by the symbol ""(or "≥") is generally called inequality.

2. Distinguish between equality and inequality: equality represents an equal relationship; Inequality represents an unequal relationship.

3. Accurately "translate" inequalities and correctly understand mathematical terms such as "non-negative number" and "not less than".

nonnegative number

Nonpositive number

Second, the basic properties of inequality

1, master the basic properties of inequality and use it flexibly:

Add (or subtract) the same algebraic expression on both sides of inequality (1), and the direction of inequality remains unchanged, that is:

If a>b, then A+C > b+c，a-c & gt； b-c。

(2) Both sides of the inequality are multiplied by (or divided by) the same positive number, and the direction of the inequality remains unchanged, that is,

If a>b and c>0, then ac> BC,

(3) When both sides of the inequality are multiplied by (or divided by) the same negative number, the direction of the inequality changes, namely:

If a>b and c < 0, ac

2. Comparison size: (A and B represent two real numbers or algebraic expressions respectively)

Generally speaking:

If a>b, then a-b is a positive number; On the other hand, if a-b is positive, then a >；; b；

If a=b, then a-b is equal to 0; On the other hand, if a-b is equal to 0, then a = b；;

If a

Namely:

a & gtb & lt= = = & gta-b & gt； 0

a = b & lt= = = & gta-b=0

aa-b & lt； 0

It can be seen that to compare the sizes of two real numbers, just look at their differences.

Third, the solution set of inequality:

1, the value of the unknown quantity that can make the inequality hold, is called the solution of the inequality; All the solutions of an inequality constitute the solution set of this inequality; The process of finding the solution set of inequality is called solving inequality.

2. There are countless solutions to inequality, generally all numbers in a certain range, which are different from the solutions of equations.

3. Representation of inequality solution set on the number axis:

When using the number axis to represent the solution set of inequality, we should determine the boundary and direction:

① Boundary: a solid circle with an equal sign and a hollow circle without an equal sign;

② Direction: large on the right and small on the left.

Four, a linear inequality:

1, the formula containing only one unknown is an algebraic expression, and the degree of the unknown is 1. Inequalities like this are called unary linear inequalities.

2. The process of solving one-dimensional linear inequality is similar to solving one-dimensional linear equation. It is particularly important to note that when both sides of the inequality are multiplied by a negative number, the sign of the inequality will change direction.

3, the steps to solve a linear inequality:

1 naming;

(2) the bracket is removed;

③ shifting items;

(4) merging similar projects;

⑤ Change the coefficient to 1 (variable inequality problem)

4. The basic situation of unary linear inequality is ax>b (or ax

① when a >; 0, the solution is;

② when a=0, b

When a=0 and b≥0, there is no solution;

③ when a

5. Exploration of inequality application (using inequality to solve practical problems)

The basic steps of solving application problems with column inequalities are similar to those of solving application problems with column equations, namely:

(1) Examination: Carefully examine the questions, find out the unequal relations in the questions, and grasp the key words in the questions, such as "greater than", "less than", "not greater than" and "not less than";

(2) setting: setting appropriate unknowns;

③ Column: list inequalities according to the inequality relations in the question;

④ Solution: Solve the solution set of the listed inequalities;

Answer: Write the answer and check whether the answer conforms to the meaning of the question.

The cultivation of mathematics learning methods and skills self-study ability is the only way to deepen learning.

When learning new concepts and operations, teachers always make a natural transition from existing knowledge to new knowledge, which is the so-called "reviewing the past and learning the new". Therefore, mathematics is a subject that can be taught by itself, and the most typical example of self-study is mathematician Hua.

We listen to the teacher's explanation in class, not only to learn new knowledge, but more importantly, to subtly influence the teacher's mathematical thinking habits and gradually cultivate our own understanding of mathematics.

The stronger the self-study ability, the higher the understanding. With the growth of age, students' dependence will be weakened, while their self-learning ability will be enhanced. So we should form the habit of previewing.

Therefore, solid mathematics learning in the past laid the foundation for future progress, and it is not difficult to learn new lessons by yourself. At the same time, when preparing a new lesson, it goes without saying that it is great to listen to the teacher explain the new lesson with questions when you encounter any problems that you can't solve.

Learn to learn, knowledge is still someone else's. The test of whether you can learn math well is whether you can solve problems. Understanding the definitions, rules, formulas and theorems related to memory is only a necessary condition for learning mathematics well, and being able to solve problems independently and correctly is the symbol of learning mathematics well.

Confidence can make you stronger.

In the exam, I always see that some students have a lot of blanks in their papers, but they haven't done a few questions at all. Of course, as the saying goes, art is bold, art is not timid. However, it is one thing to fail, and it is another thing to fail. The solution and result of a slightly more difficult math problem are not obvious at a glance. It is necessary to analyze, explore, draw, write and calculate. After tortuous reasoning or calculation, some connection between conditions and conclusions will be revealed and the whole idea will be clear.

When solving a specific problem, we must carefully examine the problem, firmly grasp all the conditions of the problem, and don't ignore any one. There is a certain relationship between a problem and a class of problems. We can think about the general idea and general solution of this kind of problem, but it is more important to grasp the particularity of this problem and the difference between this problem and this kind of problem. There are almost no identical problems in mathematics, and there are always one or several different conditions, so the process of thinking and solving problems is not the same. Some students and teachers can do the questions they have talked about, while others can't. They just talk about the matter and stare at some small changes in the problem, and they can't start.

The topics of mathematics are infinite, but the ideas and methods of mathematics are limited. As long as we learn the basic knowledge well and master the necessary mathematical ideas and methods, we can successfully deal with endless problems. The topic is not to do more, the better. The ocean of topics is endless, and you will never finish reading it. The key is whether you have cultivated good mathematical thinking habits and mastered the correct mathematical problem-solving methods.

Solving problems requires rich knowledge and more confidence. Without self-confidence, you will be afraid of difficulties and give up; With self-confidence, we can forge ahead, not give up easily, study harder, and hope to overcome difficulties and usher in our own spring.

Qingdao version of the eighth grade mathematics knowledge related articles;

★ Sort out and summarize the knowledge points of eighth grade mathematics.

★ Summary of knowledge points of eighth grade mathematics last semester

★ Summary of knowledge points in the first volume of eighth grade mathematics

★ The arrangement of mathematics knowledge points in the second volume of the eighth grade

★ The first volume of eighth grade mathematics always reviews knowledge points.

★ Mathematics knowledge points in the second volume of the eighth grade

★ Summary of the knowledge points in the first volume of the second grade mathematics.

★ Summary of the first volume of the eighth grade mathematics knowledge points and the eighth grade mathematics learning skills.

★ Summary of knowledge points in the first volume of eighth grade mathematics

★ Arrangement of knowledge points in the first volume of eighth grade mathematics

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