Seven-grade mathematics knowledge points
1. triangle: A figure composed of three line segments that are not on the same line and are connected end to end is called a triangle.
2. Classification of triangles
3. Trilateral relationship of triangle: the sum of any two sides of triangle is greater than the third side, and the difference between any two sides is less than the third side.
4. Height: Draw a vertical line from the vertex of the triangle to the line where the opposite side is located, and the line segment between the vertex and the vertical foot is called the height of the triangle.
5. midline: in a triangle, the line segment connecting the vertex and the midpoint of its opposite side is called the midline of the triangle.
6. Angular bisector: The bisector of the inner angle of a triangle intersects the opposite side of this angle, and the line segment between the intersection of the vertex and this angle is called the angular bisector of the triangle.
7. Significance and practice of high line, middle line and angle bisector.
8. Stability of triangle: The shape of triangle is fixed, and this property of triangle is called stability of triangle.
9. Theorem of the sum of interior angles of triangle: the sum of three interior angles of triangle is equal to 180.
It is inferred that the two acute angles of 1 right triangle are complementary;
Inference 2: One outer angle of a triangle is equal to the sum of two non-adjacent inner angles;
Inference 3: One outer angle of a triangle is larger than any inner angle that is not adjacent to it;
The sum of the inner angles of a triangle is half of the sum of the outer angles.
10. External angle of triangle: the included angle between one side of triangle and the extension line of the other side is called the external angle of triangle.
1 1. The Properties of the Exterior Angle of Triangle
(1) Vertex is the vertex of a triangle, one side is one side of the triangle, and the other side is the extension line of one side of the triangle;
(2) An outer angle of a triangle is equal to the sum of two inner angles that are not adjacent to it;
(3) The outer angle of a triangle is greater than any inner angle that is not adjacent to it;
(4) The sum of the external angles of the triangle is 360.
12. Polygon: On the plane, a figure composed of end-to-end line segments is called a polygon.
13. Interior angle of polygon: The angle formed by two adjacent sides of a polygon is called its interior angle.
14. Exterior angle of polygon: the angle formed by the extension line of one side of polygon and its adjacent side is called the exterior angle of polygon.
15. Diagonal line of polygon: the line segment connecting two non-adjacent vertices of polygon is called diagonal line of polygon.
Sorting out the knowledge points of mathematics in the first day of junior high school
1. Ordered number pair: a word containing two numbers represents a definite position, where each number represents a different meaning. We call this number pair consisting of two numbers A and B in the order of (A, B) (A, B), where A stands for the horizontal axis and B stands for the vertical axis.
2. Plane rectangular coordinate system: Two number axes perpendicular to each other on the same plane and having a common origin form a plane rectangular coordinate system, which is called rectangular coordinate system for short. Usually, the two number axes are placed in horizontal and vertical positions respectively, and the right and upward directions are the positive directions of the two number axes respectively. The horizontal axis is called X axis or horizontal axis, the vertical axis is called Y axis or vertical axis, and the X axis or Y axis is collectively called coordinate axis. Their common origin O is called the origin of rectangular coordinate system.
3. Horizontal axis, vertical axis and origin: the horizontal axis is called X axis or horizontal axis; The vertical axis is called Y axis or vertical axis; The intersection of the two coordinate axes is the origin of the plane rectangular coordinate system.
4. Coordinates: For any point P on the plane, the passing P is perpendicular to the X axis and Y axis respectively, and the vertical foot is on the X axis and Y axis respectively. The corresponding numbers a and b are called the abscissa and ordinate of the point p, respectively.
5. Quadrant: Two coordinate axes divide the plane into four parts, the upper right part is called the first quadrant, and the counterclockwise part is called the second quadrant, the third quadrant and the fourth quadrant. The point on the coordinate axis is not in any quadrant.
6. Coordinate characteristics of special location points
(1) The ordinate of the point on the x axis is zero; The abscissa of a point on the y axis is zero.
(2) The abscissa and ordinate of the points on the bisector of the first quadrant and the third quadrant are equal; The horizontal and vertical coordinates of the points on the bisector of the second and fourth quadrants are opposite to each other.
(3) If the abscissas of any two points are the same, the line connecting the two points is parallel to the longitudinal axis; If the vertical coordinates of two points are the same, the straight line connecting the two points is parallel to the horizontal axis.
(4) Distance from point to axis and origin.
The distance from the point to the X axis is | y | The distance from the point to the Y axis is | x | The distance from the point to the origin is the square of x plus the square of y and then open the root sign;
7. Characteristics of symmetrical points in plane rectangular coordinate system
(1) The coordinates of points that are symmetrical about the X axis have the same abscissa and the opposite ordinate. (horizontal and vertical)
(2) With regard to the coordinates of Y-symmetric points, the ordinate is the same and the abscissa is the opposite number. (horizontal and vertical)
(3) With regard to the coordinates of a point whose origin center is symmetrical, the abscissa and the ordinate are reciprocal, and the ordinate and the ordinate are reciprocal. (Horizontal and vertical directions)
8. The law of points and coordinates on each quadrant and coordinate axis
The first quadrant: (+,+) is positive.
The second quadrant: (-,+) negative and positive
The third quadrant: (-,-) negative.
The fourth quadrant: (+,-) plus or minus
Positive direction of X axis: (+,0)
Negative direction of X axis: (-,0)
Positive direction of Y axis: (0,+)
Negative direction of Y axis: (0,-)
The ordinate of the point on the X axis is 0, and the abscissa of the point on the Y axis is 0.
Origin: (0,0)
Note: Points in the coordinate system in the form of pairs (x, y) (e.g. 2, -4), where "2" is the x-axis coordinate and "-4" is the y-axis coordinate.
Seven-grade mathematics knowledge points
1 The problem of planting trees on unclosed lines can be divided into the following three situations:
(1) If trees are to be planted at both ends of the non-closed line, then: number of plants = number of segments+1= total length ÷ plant spacing-1 = total length ÷ (number of plants-1).
2 If you want to plant trees at one end of the unclosed line and not at the other end, then:
Number of plants = number of segments = total length/plant spacing = plant spacing × plant number = total length/plant number
(3) If no trees are planted at both ends of the non-closed line, then:
Number of plants = number of nodes-1= total length ÷ plant spacing-1 total length = plant spacing × (number of plants+1) plant spacing = total length ÷ (number of plants+1)
2 The quantitative relationship of planting trees on the closed line is as follows: number of trees = number of segments = total length ÷ plant spacing = plant spacing × number of trees = total length ÷ number of trees profit and loss problem.
(Profit+Loss) ÷ Difference between two distributions = number of shares participating in distribution.
(Big profit-small profit) ÷ Difference between two distributions = number of shares participating in distribution.
(big loss-small loss) ÷ The difference between the two distributions = the number of shares participating in the distribution meets the problem.
Encounter distance = speed and x Meet time = Meet distance ÷ Sum of speed and speed = Meet distance ÷ Meet time tracking problem.
Catch-up distance = speed difference × catch-up time = catch-up distance ÷ speed difference = catch-up distance ÷ catch-up time flow.
Downstream velocity = still water velocity+countercurrent velocity = still water velocity-water velocity = (downstream velocity+countercurrent velocity) ÷2 Water velocity = (downstream velocity-countercurrent velocity) ÷2 Concentration problem
Solute weight+solvent weight = solution weight ÷ solution weight × 100%= concentrated solution weight × concentration = solute weight ÷ concentration = solution weight profit and discount problem profit = selling price-cost.
Profit rate = profit/cost × 100%= (selling price/cost-1)× 100%.
Up and down amount = principal × up and down percentage
Discount = actual selling price/original selling price × 100% (discount
1km =1000m1mm =1mm =10cm1mm =10cm/kloc-0. 8+00000 m2 1 m2 = 100 m2/m2 = 1 00 m2 1 m2 = 100 m2 (volume) product unit conversion 1 m3 =
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