Main attributes:

The sum of any two sides of a (1) triangle is greater than the third side.

(2) The sum of the three internal angles of a triangle is equal to 180. The outer angle of a triangle is equal to the sum of its two non-adjacent inner angles.

(3) The corresponding edges of congruent triangles are equal, and the corresponding angles are equal.

(4) Two triangles correspond to congruences of three equilateral sides (abbreviated as "sides" or "SSS"); There is an angle, and both sides of the angle are congruent (referred to as "corner edge" or "SAS"); The congruence of two triangles with two angles and the sides corresponding to these two angles (referred to as "angle" or "ASA" for short); Two triangles (abbreviated as "corner edge" or "AAS") with two angles and the opposite sides of one angle are congruent.

(5) The distance between the point on the vertical line in the line segment and the two end points of the line segment is equal. The point on the bisector of an angle is equal to the distance on both sides of the angle.

Chapter 2: Graphics and Transformation

Main attributes

(1) The axis of symmetry bisects the line segment connecting the two symmetrical points vertically, and the shape and size of the graph do not change with the axisymmetric transformation.

(2) Translation transformation does not change the shape, size and direction of the figure, and the line segments connecting the corresponding points are parallel and equal.

(3) The rotation transformation does not change the size and shape of the figure, the distances between the corresponding points and the rotation center are all equal, and the angles formed by the connecting lines between the corresponding points and the rotation center are all equal to the rotation angle.

(4) Similarity transformation does not change the size of each corner in the graph; Each line segment in the diagram is enlarged (or reduced) by the same multiple.

Chapter III: Possibility of events

(1) An inevitable event under certain conditions is called an inevitable event; Under certain conditions, the inevitable events are called impossible events; Under certain conditions, events that may or may not occur are called uncertain events (or random events).

(2) Mathematically, the probability of an event is also called the probability of an event. The probability of inevitable events is 1 or 100%, the probability of impossible events is 0, and if p is used to represent the probability of uncertain events, it is 0 < p < 1.

The fourth chapter:

An equation containing two unknowns and terms whose unknowns are once is called a binary linear equation, and the values of a pair of unknowns that make both sides of the binary linear equation equal are called the solutions of the binary linear equation.

An equation group consisting of two linear equations and containing two unknowns is called a binary linear equation group. At the same time, the solution of each equation in binary linear equations is called the solution of binary linear equations.

Basic idea

Two-dimensional linear equation elimination one-dimensional linear equation

Steps to solve practical problems by using equations

Understand the problem (investigate the problem, clarify the known and unknown, and analyze the quantitative relationship)

Make a plan (consider how to set elements and list equations according to equivalence relation)

Execute the plan (list the equations and solve them to get the answer)

Review (check and reflect on the problem-solving scale to check the correctness of the answer and whether it conforms to the meaning of the question)

Main methods and skills

Solving binary linear equations by substitution method and addition and subtraction method

Solving simple practical problems by using binary linear equations

chapter five

Exponential Power of Integer and Its Basic Operation Principle

Multiplication law of algebraic expressions

Multiply the monomial with the monomial, respectively, by their coefficients and the same base, and the remaining letters, together with their exponents, remain unchanged as the factors of the product.

Multiplying a polynomial by a monomial is to multiply each term of a polynomial by a monomial, and then add the products.

Polynomials multiply polynomials by multiplying each term of one polynomial with each term of another polynomial, and then adding the products.

Division law of algebraic expressions

In monomial division, the coefficient and the power of the same base number are separated as a factor of the quotient, and the letter only contained in the division formula, together with its exponent, is taken as a factor of the quotient.

Polynomial divided by monomial, first divide each term of this polynomial by this monomial, and then add the obtained quotients.

Chapter vi

The numerator and denominator of the 1. fraction are all multiplied (or divided) by the same non-zero algebraic expression, and the value of the fraction remains unchanged. that is

Where m is an algebraic expression that is not equal to zero.

2. Fractions are multiplied by fractions, with the product of molecules as the numerator of the product and the product of denominator as the denominator of the product; Fraction is divided by fraction, and numerator and denominator of divisor are multiplied by divisor in turn.

3. Add and subtract fractions with the same denominator, and add and subtract molecules with the same denominator.

4. Fractions with different denominators are divided into fractions with the same mother number, which is called general fractions. After general division, the addition and subtraction of fractions with different denominators is converted into the addition and subtraction of fractions with the same denominator.

5. To solve the fractional equation, you need to try the roots. Substitute the obtained root into the original equation or the common denominator of multiplication on both sides of the original equation, so the root with zero score is called increasing root and must be discarded.

Review outline of seventh grade mathematics next semester;

I. Conceptual knowledge

1, monomial: The product of numbers and letters is called monomial.

2. Polynomial: The sum of several monomials is called polynomial.

3. Algebraic expressions: monomials and polynomials are collectively referred to as algebraic expressions.

4. The number of monomials: The sum of the indices of all the letters in the monomials is called the number of monomials.

5. Degree of Polynomial: The degree of the term with the highest degree in the polynomial is the degree of the polynomial.

6. Complementary angle: The sum of two angles is 90 degrees, and these two angles are called complementary angles.

7. Complementary angle: The sum of two angles is 180 degrees, and these two angles are called complementary angles.

8. Relative vertex angles: two corners have a common vertex, and two sides of one corner are opposite to the extension lines of two sides of the other corner. These two angles are antipodal angles.

9. Common angle: In the "three-line octagon", the angles at the same position are common angles.

10, internal angle: in the "three-line octagon", the angle sandwiched between two straight lines is the internal angle.

1 1, ipsilateral inner angle: in "trilinear octagon", the angle on the same side of trilinear is ipsilateral inner angle.

12, significant number: an approximation, starting with the first number on the left that is not 0 and ending with the exact 1, all numbers are significant numbers.

13, probability: the probability of an event is the probability of this event.

14, triangle: A figure composed of three line segments that are not on the same line is called a triangle.

15, Angle bisector of triangle: In a triangle, the angle bisector of an inner angle intersects its opposite side, and the line segment between the intersection of the vertex and this angle is called the angle bisector of triangle.

16, triangle midline: the line segment connecting the vertex and the midpoint of the opposite side of the triangle is called the midline of the triangle.

17. Height line of triangle: Draw a vertical line from one vertex of triangle to the line where its opposite side is located, and the line segment between vertex and vertical foot is called height line of triangle.

18, congruent graphics: two graphics that can overlap are called congruent graphics.

19, variable: the number of changes is called variable.

20. Independent variable: If there is an active change in the amount of change, it is called an independent variable.

2 1, dependent variable: the quantity that changes passively with the change of independent variables is called dependent variable.

22. Axisymmetric figure: If a figure is folded along a straight line and the parts on both sides of the straight line can overlap each other, then this figure is called an axisymmetric figure.

23. Symmetry axis: A straight line folded in half in an axisymmetric figure is called symmetry axis.

24. perpendicular bisector: The line segment is an axisymmetric figure, and its symmetry axis is perpendicular to this line segment and divides it into two parts. Such a straight line is called the midline of this line segment. (refers to the middle vertical line)

Second, computing power.

(a) Calculation of algebraic expressions.

1, addition and subtraction of algebraic expressions

Remove brackets and merge similar items!

2. Power operation (seven formulas)

① Power with the same base: the base is constant, and the exponents are added. (2) Power of power: the base number is unchanged, multiplied by the index.

③ Power of product: equal to the product of the power of each element. (4) Multiply with exponential power: the exponent is constant and the base is multiplied.