Knowledge points in the first volume of eighth grade mathematics: Chapter 11 congruent triangles 1. The nature of congruent triangles: congruent triangles has equal sides and angles.
2. congruent triangles's judgment: three sides are equal (SSS), two sides are equal to their included angle (SAS), two angles are equal to their sandwiched edge (ASA), two angles are equal to the opposite side of an angle (AAS), and two right-angled triangles are equal to their hypotenuse and right-angled edge (HL).
3. The nature of the angle bisector: the angle bisector bisects this angle, and the distance from the point on the angle bisector to both sides of the angle is equal.
4. Inference of the bisector of the angle: The point where the distance from the inside of the angle to both sides of the angle is equal is called the bisector.
5. The basic method steps to prove the congruence of two triangles or to prove the equality of line segments or angles with it: ①. Determine the known conditions (including implied conditions, such as common * * * edge, common * * * angle, diagonal, bisector of angle, median line, height, isosceles triangle and other implied angular relations. ); 2. Review the triangle judgment and find out what else we need; ③.
The knowledge points in the first volume of eighth grade mathematics (1) are axisymmetrical.
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, the height on the bottom edge and the midline on the bottom edge of the isosceles triangle coincide. Three lines in one? .
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.
There is a 60-degree angle? An isosceles triangle is an equilateral triangle.
There are two angles that are 60? Our triangle is an equilateral triangle.
13. In a right triangle, 30? The right angle of an angle is equal to half of the hypotenuse.
14. The midline of the hypotenuse of a right triangle is equal to half of the hypotenuse.
The eighth grade mathematics knowledge points Volume 1 (2) 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 as y=kx+b(k? 0), say 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. The general formula of proportional sequence function: y=kx(k? 0), whose image is a straight line passing through the origin (0,0).
5. Proportional column 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).