Geometry knowledge point 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.
The formula of addition and subtraction 1 of algebraic expressions, that is, the product of numbers or letters, is called a monomial, and a single number or letter is also a monomial.
2. The numerical factor in a single item is called the coefficient of the item.
3. In the monomial, the sum of the indices of all letters is called the number of times of the monomial.
4. the sum of several monomials is called polynomial, in which each monomial is called $ term of polynomial and the term without letters is called constant term.
5. The degree of the highest term in a polynomial is called the degree of a polynomial.
6. Merging similar terms in polynomials into one term is called merging similar terms. After merging similar items, the coefficient of the obtained item is the sum of the coefficients of similar items before merging, and the letter part remains unchanged.
7. If the factor outside the brackets is positive, the symbols of the items in the original brackets are the same as the original symbols after removing the brackets.
8. If the factor outside the brackets is negative, the symbols of the items in the original brackets are opposite to those after the brackets are removed.
9. Generally speaking, several algebraic expressions are added and subtracted. If there are brackets, remove them first, and then merge similar items.
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.
Decomposition factor 1. Formula: 1, ma+MB+MC = m (a+b+c);
2、a2-B2 =(a+b)(a-b)；
3、a22ab+b2=(ab)2 .
Second, turn a polynomial into the product of several algebraic expressions. This deformation is called decomposition of this polynomial.
1, the product of several algebraic expressions becomes a polynomial form, which is a multiplication operation.
2. Turning a polynomial into the product of several algebraic expressions is factorization.
3.ma+mb+mcm(a+b+c)4。 Factorization and algebraic expression multiplication are deformations in opposite directions.
3. Let all terms of a polynomial contain the same factor, which is called the common factor of each term of this polynomial. To decompose a factor by the common factor method is to convert a polynomial into a monomial and then multiply it with this polynomial. The general steps to find the common factor are: (1) If each coefficient is an integer coefficient, take the greatest common factor of the coefficient; (2) Taking the same letter, the index of the letter is lower; (3) Take the same polynomial with lower exponent. (4) The product of all these factors is the common factor.
4. The general steps of factorization are as follows: (1) If there is-first extract-,if each polynomial has a common factor, then extract the common factor. (2) If each polynomial has no common factor, choose the square difference formula or the complete square formula according to the characteristics of the polynomial. (3) Every polynomial must be decomposed until it can no longer be decomposed.
5. A formula in the form of A2+2ab+b2 or a2-2ab+b2 is called a completely flat mode.
Factorization method: 1, common factor method. 2. Formula method.