Axisymmetric knowledge points 1. If a graph is folded along a straight line and the parts on both sides of the straight line can overlap each other, then the graph is called an axisymmetric graph; This straight line is called the axis of symmetry.
2. The symmetry axis of an axisymmetric figure is the perpendicular bisector of a line segment connected by any pair of corresponding points.
3. The distance from the point on the bisector of the angle is equal to both sides of the angle.
4. The distance between any point on the vertical line of the line segment and the two endpoints of the line segment is equal.
5. The point with equal distance from the two endpoints of a line segment is on the middle vertical line of this line segment.
6. The corresponding line segment and the corresponding angle on the axisymmetric figure are equal.
7. Draw an axisymmetric figure about a straight line: find the key points, draw the corresponding points of the key points, and connect the points in the original order.
8. The coordinates of the point (x, y) about the axis symmetry of X are (x, -y).
The coordinates of the point (x, y) that is symmetric about y are (-x, y).
The coordinates of the point (x, y) that is symmetrical about the origin are (-x, -y).
9. The nature of isosceles triangle: the two base angles of isosceles triangle are equal (equilateral and equiangular).
The bisector of the top angle of an isosceles triangle, the height on the bottom edge and the midline on the bottom edge coincide, which is called the integration of the three lines for short.
10. Determination of isosceles triangle: equilateral and equilateral.
1 1. The three internal angles of an equilateral triangle are equal and equal to 60.
12. Determination of equilateral triangle: A triangle with three equal angles is an isosceles triangle.
An isosceles triangle with an angle of 60 is an equilateral triangle.
A triangle with two angles of 60 is an equilateral triangle.
13. In a right triangle, the right angle side of 30 is equal to half of the hypotenuse.
Data analysis 1. Weighted average: the calculation formula of weighted average. Understanding of weight: It reflects the importance of a certain data in the whole data. But in the form of ratio or percentage, the weighted average value is obtained by using the frequency distribution table.
2. Arrange a set of data in order from small to large (or from large to small). If the number of data is odd, the middle number is the median of this set of data; If the number of data is even, the average of the middle two data is the median of this set of data.
3. The data with the highest frequency in a set of data is the pattern of this set of data.
4. The difference between the maximum data and the minimum data in a set of data is called the extreme range of this set of data.
5. The greater the variance, the greater the data fluctuation; The smaller the variance, the smaller the data fluctuation and the more stable it is.
Inequality 1. Grasp 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 the same, that is, if A >；; B, then a+c > b+c，a-c & gt； b-c .
(2) if both sides of the inequality are multiplied by (or divided by) the same positive number, the direction of the inequality remains unchanged, that is, if a >；; B and c>0, then AC & GT200 BC.
(3) If both sides of the inequality are multiplied by (or divided by) the same negative number, the direction of the inequality will change, that is, 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>b<= = = & gta-b & gt；; 0; a = b & lt= = = & gta-b = 0； a & ltb & lt= = = & gta-b & lt； 0。
3. Solution set of inequality: the value of unknown quantity that can make inequality hold is called the solution of 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.
4. Representation of the inequality solution set on the number axis: When the inequality solution set is represented by the number axis, the boundary and direction should be determined: ① Boundary: there are solid circles with equal signs and hollow circles without equal signs; ② Direction: large on the right and small on the left.
Geometry knowledge points 1. Rotation and translation
Translation and rotation are important ways of congruent transformation in geometry, and rotation is a common means to examine everyone's ability to change geometry.
The problem of rotation is difficult because he makes many equilateral angles appear in the graph through rotation, but this is not directly spoken in the graph and needs to be discovered by everyone themselves. The combination of rotation with quadratic function, inverse proportional function, quadrilateral and other knowledge will make the topic very flexible, so we must firmly grasp this piece when learning basic knowledge.
2. Parallelogram
Parallelogram is the basis of learning rectangle, diamond and square. There are five ways to judge. In practical application, it is often difficult for students to decide which way to take, which requires students to choose flexibly according to the graph and solve it in different ways.
3. Special parallelogram rows
Special parallelogram is the content of grade three, but it is mentioned in many places as grade two. This part of knowledge is flexible and difficult to synthesize, which is often the beginning for students to find geometry difficult to learn. The solution is to write out their nature and judgment list, because the expressions are very similar and close, which is difficult to remember. This requires students to use the method of comparative analysis to find out the respective properties and judgments of these three graphics, so as to avoid confusion in application.