2. Angle: A figure composed of two rays drawn from a point is called an angle.
3. The size of the angle: The size of the angle depends on the size of both sides. The bigger the fork, the bigger the angle.
4. The unit of measuring angle: degree, which is indicated by the symbol "0".
5. An angle less than 90 is called an acute angle; An angle greater than 90 and less than180 is called an obtuse angle. The angle between two sides in a straight line is called a right angle. Boxer 180.
6. Vertical line: When two straight lines intersect at right angles, they are perpendicular to each other, one of which is the vertical line of the other, and the intersection of these two straight lines is called vertical foot. (Description of drawings)
7. Parallel lines: Two straight lines that do not intersect on the same plane are called parallel lines. It can also be said that these two straight lines are parallel to each other.
(Illustration) The vertical line segments between parallel lines are all equal in length.
8. Triangle: A figure surrounded by three line segments is called a triangle.
9. The classification of triangle:
(1) By angle: acute triangle, obtuse triangle, right triangle.
(2) Divided by sides: general triangle, isosceles triangle and equilateral triangle.
10. The sum of the three internal angles of a triangle is 180.
Quadrilateral: a figure surrounded by four line segments.
12. The circle is a curve figure. The distance from any point on the circle to the center of the circle is equal, and this distance is the length of the radius of the circle.
13. There are countless circles in radius and diameter. The diameter of the same circle is twice the radius, and the radius is half the diameter.
14. Axisymmetric graph: If a graph is folded in half along a straight line, two graphs of the straight line can completely overlap, and this graph is an axisymmetric graph. The straight line where the crease lies is called the symmetry axis.
15. The axisymmetric figures in the learned figures are: circle, isosceles triangle, equilateral triangle, rectangle, square and isosceles trapezoid.
16. Perimeter: The sum of all the side lengths surrounding a graph is the circumference of the graph.
Area: The size of an object's surface or closed plane figure is called their area.
17。 Surface area: The sum of all the areas of a three-dimensional figure is called the surface area of this three-dimensional figure.
Volume: The size of the space occupied by an object is called the volume of the object.
18. Both cuboids and cubes have 12 sides, 6 faces and 8 vertices.
A cube is a special cuboid and an equilateral triangle is a special isosceles triangle.
19. Three characteristics of the cylinder: (1) The thickness of the top and bottom is the same; (2) The side is curved; (3) The two bottom surfaces are the same circle.
20. Height of cylinder: The distance between two bottom surfaces of cylinder is called the height of cylinder. A cylinder has countless heights, all of which are parallel and equal.
2 1. Expand the side of the cylinder to get a rectangle. The length of this rectangle is equal to the circumference of the bottom of the cylinder, and the width is equal to the height of the cylinder.
22.Pi π is an infinite acyclic decimal. π=3. 14 1592653……
23. Divide the circle into several parts, and the figure is close to a rectangle. The length of this rectangle is half of the circumference, and the width is the radius of the circle.
24. Height of the cone: The distance from the apex of the cone to the center of the bottom surface is the height of the cone.
25. The volume of a cone with equal bottom and equal height is cylindrical, and the volume of a cylinder with equal bottom and equal height is three times that of a cone.
For cylinders and cones with equal volume and bottom area, the height of the cylinder is conical and the height of the cone is three times that of the cylinder.
Nine. Ratio and proportion
Meaning of 1. ratio: The division of two numbers is also called the ratio of two numbers.
Meaning of proportion: Two expressions with equal proportions are called proportions.
2. Find the ratio: the quotient obtained by dividing the former term of the ratio by the latter term of the ratio is called the ratio.
3. The basic nature of the ratio: the first term and the second term of the ratio are multiplied or divided by the same number (except 0), and the ratio remains unchanged.
The basic property of proportion: in proportion, the product of two external terms is equal to the product of two internal terms.
4. The basic properties of application ratio can be simplified;
Using the basic properties of proportion, we can judge whether two proportions can form a proportion, and we can also find out the unknown term in the proportion, that is, the solution ratio.
5. Use letters to express the relationship between ratio and division and fraction.
a:b=a÷b= (b≠0)
6. Scale: We call the ratio of the distance on the map to the actual distance the scale of this map.
7. Distance on the map: actual distance = proportion
Or = scale
Actual distance = distance on the map/distance on the scale map = actual distance × scale.
8. Method of finding the ratio: According to the meaning of the ratio, divide the former item by the latter item, and the result is a number.
Method of simplifying the ratio: According to the basic properties of the ratio, multiply or divide the first and second terms of the ratio by the same number (except zero), and the result is the simplest integer ratio.
9. Proportional relationship: two related quantities, one change and the other change. If the ratio (that is, quotient) of the corresponding two numbers in these two quantities is certain, these two quantities are called proportional quantities, and their relationship is called proportional relationship.
Use the formula: =k (certain), and graphically illustrate that the proportional relationship is a straight line.
10. Inverse relationship: two related quantities, one changes and the other changes. If the product of the corresponding two numbers in these two quantities is certain, then these two quantities are called inverse proportional quantities, and their relationship is called inverse proportional relationship.
Expressed by formula: x×y=k (definite), graphically expressed, and the inverse ratio relationship is a curve.
Simple statistics
1. Common statistical charts include bar chart, line chart and fan chart.
2. Features of bar graph: (1) A certain quantity is expressed by unit length. (2) Use the length of the straight bar to express the quantity. Function: From the figure, we can clearly see the figures of each quantity for comparison.
Features of broken-line statistical chart: (1) A certain quantity is expressed by unit length. (2) The fluctuation of broken lines indicates the increase or decrease of quantity. Function: you can clearly see the change of quantity and quantity from the picture.
Arrangement of eleven formulas
Plane graphics:
1. rectangle:
Circumference = (length+width) ×2 C Length =(a+b)×2
Area = length × width s Length =a ×b
2. Square:
Perimeter = side length ×4 C plus =a×4
Area = side length × side length s positive =a×a
3. The area of parallelogram = base × height s flat =ah.
4. Area of triangle = base × height ÷2 S =ah÷2.
5. Trapezoidal area = (upper bottom+lower bottom) × height ÷2 S step =(a+b)×h÷2.
6. The circumference of a circle = diameter ×3. 14 C circle = π d.
Circumference of a circle = radius ×2×3. 14 C circle = 2π r.
Area of circle = square of radius ×πs circle =πr2.
Three-dimensional graphics:
1. cuboid
Surface area = (length × width+length × height+width × height) ×2 S Long table =(ab+ah+bh)×2
Volume = length x width x height v length =abh
2. Cubic
Surface area = side length × side length× 6 s front surface =a×a×6
Volume = side length x side length x side length v positive =a3
Step 3: Cylinder
Transverse area = bottom circumference × height.
Surface area = side area+two bottom areas.
Volume = bottom area × height
4. The surface area and volume of the above three-dimensional figure can be unified into the formula:
Surface area = perimeter of bottom surface × height+volume of two bottom areas = bottom area × height
border area/region
5. The volume of the cone = the volume of the cylinder ÷3 V cone =sh÷3