Eighth grade mathematics knowledge point book 1
1, the corresponding edge of congruent triangles is equal to the corresponding angle.
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.
Knowledge points of the first semester of junior two mathematics
real number
Arithmetic square root: Generally speaking, if the square of a positive number X is equal to A, that is, x2=a, then this positive number X is called the arithmetic square root of A, and the arithmetic square root recorded as .0 is 0. By definition, A has an arithmetic square root only when a≥0. ※.
Square root: Generally speaking, if the square root of a number X is equal to A, that is, x2=a, then this number X is called the square root of A. ※ 。
A positive number has two square roots (one positive and one negative), which are opposite to each other. 0 has only one square root, which is itself. ※: Negative numbers have no square root.
The cube root of a positive number is a positive number. The cube root of 0 is 0. ※: The cube root of a negative number is a negative number.
The inverse of a is -a, the absolute value of a positive real number is itself, the absolute value of a negative number is its inverse, and the absolute value of 0 is 0.
linear function
1. General steps for drawing function images: 1. List (one function only needs two points at a time, other functions generally need more than five points, and the listed points are independent variables and their corresponding function values); 2. Draw points (in rectangular coordinate system, draw four points in the table with the value of independent variable as abscissa and the value of corresponding function as ordinate, generally a function only needs two points at a time); 3.
2. Write the resolution function according to the meaning of the question: the key is to find the equivalent relationship between the function and the independent variable, and list the equations, that is, the resolution function.
3. If the relationship between two variables X and Y can be expressed in the form of y=kx+b(k≠0), then Y is a linear function of X (X is the independent variable and Y is the dependent variable). In particular, when b=0, y is said to be a proportional function of x 。
4. General formula of proportional sequence function: y=kx(k≠0), which is like a straight line passing through the origin (0,0).
5. The image of the proportional sequence function y=kx(k≠0) is a straight line passing through the origin. When k >: 0, the straight line y=kx passes through the first and third quadrants, and y increases with the increase of X. When k < 0, the straight line y=kx passes through the second and fourth quadrants, and y decreases with the increase of X. In the linear function y=kx+b, when k >; 0, y increases with the increase of x; When k < 0, y decreases with the increase of x 。
6. Find the resolution function of two known coordinates (resolution function of undetermined coefficient method):
Bring two points into the general formula of the function and list the equations.
Find the undetermined coefficient
Bring the undetermined coefficient value into the general formula of the function and get the analytic function.
7. From the function image, we will find the solution of the linear equation of one variable (i.e. the abscissa value of the coordinate of the intersection point with the X axis), the solution set of the linear inequality of one variable and the solution of the linear equation of two variables (i.e. the coordinate value of the intersection point of two functions).
Math learning methods and skills in junior two.
Pre-math preparation for junior and middle schools.
If junior high school students want to learn math well, they should use the time before class to preview what the teacher will say in class. Pre-class preparation of junior high school mathematics is to understand what the teacher said in class, which is beneficial to junior high school students to organize their own knowledge structure and convenient.
Junior high school students can also learn what they don't understand by previewing mathematics before class, so that they will concentrate on listening in class and won't slip away and be distracted. At the same time, preview before class can also form a system of knowledge points, which can help junior high school students establish a complete knowledge structure.
Mathematics in junior and middle schools is the key.
Junior high school students want to learn students well, and class is a word: follow. Keep up with the teacher in junior high school math class. The teacher must keep up with where he talks, look at the teacher's blackboard carefully, and always know where the teacher talks and what the knowledge points are. Some junior high school students like to take notes, so I want to remind you not to take notes in junior high school math class.
Your main purpose is to follow the teacher, not just take notes. Even if there is something you can't do, you should write it down quickly and concisely, and you can improve it after class. It is most important to keep up with the teacher's thinking, which means that you understand the teacher's analysis and problem-solving process.
You can do some basic math problems in junior high school after class.
After each class, junior high school students can do some basic problems of junior high school mathematics after class. When doing this kind of problem, I suggest that you don't make mistakes, and learn to think and organize after you finish the problem. When there is no problem with your basic math problems in junior high school, you can do some difficult upgrading problems. If you can't do it, you can look at it according to the analysis.
But remember never to do this kind of problem in large quantities. It is helpful for junior high school students to do difficult problems occasionally, but it is not good to concentrate. At the same time, we should learn to sort out and summarize our mistakes.
Mathematics is developed from simple things step by step, so as long as people who study mathematics understand it honestly and step by step, and remember its main points for later use, they will certainly understand all its contents. In other words, if they understand the first step, they will certainly understand the second step, the first step and the second step, and they will certainly understand the third step. It's like a ladder class. As long as his legs are long enough to cross the first step, he will certainly be able to climb from the first step to the second step, and from the second step to the third and fourth steps ... At this time, he just does the same thing over and over again, so anyone should be able to do it.
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