Congruent triangles 1. basic concept
Two triangles that can completely coincide are called congruent triangles.
2. The nature of congruent triangles
(1) The corresponding edges of congruent triangles are equal; (2) The angles corresponding to congruent triangles are equal;
3. congruent triangles's judgment method
(1) Two triangles with equal sides are congruent; (2) The two corners and their clamping edges are congruent with each other;
(3) The opposite sides of two angles and one angle correspond to the congruences of two equal triangles; (4) Two triangles with equal angles between two sides; (5) The hypotenuse and the right-angled side correspond to the congruence of two right-angled triangles.
2. The nature and judgment of angular bisector.
Property: the distance from a point on the bisector of an angle to both sides of the angle is equal;
Judgment: The points with equal distance to both sides of an angle are on the bisector of this angle.
Axisymmetric 1. axial symmetric figure
A figure is folded in half along a straight line, and the parts on both sides of the straight line can completely overlap. This straight line is called the axis of symmetry. Points that coincide with each other are called corresponding points.
2. Axisymmetric
Two figures are folded in half along a straight line, and one of them can completely coincide with the other. This straight line is called the axis of symmetry. Points that coincide with each other are called corresponding points.
3. The difference and connection between axisymmetric graphics and axisymmetric graphics.
(1) Difference: Axisymmetric refers to the positional relationship between two graphs, and axisymmetric graphs refer to graphs with special shapes; Axisymmetric involves two figures, and the axisymmetric figure is aimed at one figure.
(2) Connection: If an axisymmetric figure is divided into two figures along the axis of symmetry, then the two figures are symmetrical about this axis; If two symmetrical figures are regarded as a whole, then it is an axisymmetric figure.
3. perpendicular bisector of the line segment
The midline property of the line segment: the distance between the point on the midline of the line segment and the two endpoints of the line segment is equal.
On the other hand, the point with equal distance from the two endpoints of a line segment is on the middle vertical line of this line segment.
4. Make an axisymmetric figure
All (1) geometric figures can be regarded as being composed of points. We only need to make the corresponding points of these points about the axis of symmetry, and then connect these points to get the axisymmetric figure of the original figure.
(2) For some graphs composed of straight lines, line segments or rays, as long as the symmetrical points of some special points (such as the end points of line segments) in the graph are made and connected, the axisymmetric graph of the original graph can be obtained.
(3) Axis symmetry is expressed in coordinates.
The coordinates of the point (x, y) which is symmetrical about the X axis 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) symmetrical about the origin are (-x, -y).
Real number 1 square root
1. definition: if the square of a number x is equal to a, that is, x? =a, then this number x is called the square root of a,
We call x the square of a (also called the square root) and write it as x = √ a.
2. Nature
(1) A positive number has two square roots in opposite directions;
(2)0 has only one square root, which is 0 itself; ?
(3) Negative numbers have no square root.
2. Cubic root
1. Definition: Generally speaking, if the cube of the number X is equal to A, that is, x3=a, then this number X is called the cube root of A (also called the cube root), which is recorded as 3 √a and read as the cube root number A. If 3 √23=8, then 2 is the cube root of 8, and the cube root of 0 is 0.
2. Property: positive number of cube root of positive number; The cube root of 0 is 0; The cube root of a negative number is a negative number. The cube root is its own number: 0, 1,-1.
Linear function 1. Variables and functions
(1) variable: a quantity that can take different values in the process of change. Constant: a quantity that can only take the same value in the process of change.
(2) Function: Generally speaking, in a changing process, if there are two variables X and Y, and for each certain value of X, Y has a unique definite value corresponding to it, then we call X an independent variable, Y a dependent variable and Y a function of X. ..
(3) Domain: The range that the independent variable of a function can take is called the domain of the function.
2. Linear function
Definition of (1) linear function: Generally, a function in the form of y=kx+b(k, b is a constant, k≠0) is called a linear function. When b=0, y=kx+b means y=kx, so the proportional function is a special linear function. Pay attention to point A. B, and the proportional coefficient k ≠ 0; C, the constant term is dispensable.
(2) The image of the linear function y=kx+b is a straight line, which we call y=kx+b, and can be regarded as the translation of the unit length of the straight line y=kx │b│ (when b>0, translate upward; When b<0, translate downward).
(3) The significance of coefficient K: K represents the inclination of straight lines, and straight lines with the same K value are parallel to each other, while straight lines with different K values intersect. Significance of coefficient b: b is the ordinate of the intersection of a straight line and the y axis. When k>0, the straight line y=kx+b rises from left to right, that is, Y also increases with the increase of X. When k < 0, the straight line y=kx+b decreases from left to right, that is, Y decreases with the increase of X. The intersection of the straight line y=kx+b and the Y axis is point (0, b). The intersection with the X axis is the point (-b/k, 0).
Multiplication, division and factorization of algebraic expressions 1. Multiplication of algebraic expressions.
(1) Multiplication rule of monomial: Multiply the monomial by its coefficient and the same letter respectively. For a letter contained only in a monomial, together with its exponent, it is a factor of the product.
(2) Polynomial multiplied by monomial is the distribution law of multiplication and addition, which is converted into monomial multiplied by monomial, that is, polynomial multiplied by monomial, and then the obtained products are added.
(3) Polynomial multiplied by polynomial. Multiply each term in one polynomial by each term in another polynomial, and then add the products.
2. Multiplication formula
(1) square difference formula:
a 2 -b 2 =(a+b)(a-b)
(2) Complete square formula:
(a b) 2 =a 2 2ab+b 2
3. Division of algebraic expressions
(1) monomial division, which is divided by the coefficient and the same base power respectively, as the factor of quotient; For letters contained only in the division formula, they are used as factors of quotient together with their subordinates.
(2) Polynomial divided by monomial, first divide each term of this polynomial by monomial, and then add the obtained quotients.
The above are the knowledge points of the first book of second-grade mathematics that I compiled, hoping to help you.