A summary of mathematical geometry knowledge points in the first volume of junior high school?

In order to help students learn mathematical geometry better and improve their mathematics scores, the following are the knowledge points of mathematical geometry in the first volume of junior high school that I share with you. I hope it can help you!

Knowledge points of mathematical geometry in the first volume of the first volume

1. Geometric figures: Points, lines, surfaces, and bodies can help people effectively depict the intricate world. They are all called geometric figures. Various figures abstracted from real objects are collectively called geometric figures. Some geometric figures whose parts are not in the same plane are called solid figures. Some geometric figures have all parts in the same plane, which are called plane figures. Although three-dimensional figures and plane figures are two different types of geometric figures, they are related to each other.

2. Classification of geometric figures: Geometric figures are generally divided into three-dimensional figures and plane figures.

3. Straight line: The basic concept of geometry is the trajectory of a point moving in the same or opposite direction in space. From the perspective of plane analytic geometry, a straight line on a plane is a figure represented by a linear equation of two variables in the plane rectangular coordinate system. To find the intersection of two straight lines, you only need to solve the two linear equations of two variables simultaneously. When the system of simultaneous equations has no solution, the two straight lines are parallel; when there are infinite solutions, the two straight lines coincide; when there is only one solution, Two straight lines intersect at a point. The angle between a straight line and the positive direction of the X-axis is often called the inclination angle of the straight line or the tangent of the angle is called the slope of the straight line to express the straight line on the plane for the X-axis degree of inclination.

4. Ray: In Euclidean geometry, the figure formed by a point on a straight line and the part beside it is called a ray or a half-line.

5. Line segment: refers to one or more different line elements forming a continuous or discontinuous graph line, such as a solid line segment or a line segment composed of "long dash, short interval, dot, short interval, dot, "Short interval" is a line segment composed of double dots and long dashes.

A line segment has the following properties: the shortest line segment between two points.

6. The distance between two points: The length of the line segment connecting two points is called the distance between the two points.

7. Endpoints: Two points on a straight line and the part between them are called line segments. These two points are called the endpoints of the line segment.

A line segment is represented by letters representing its two endpoints or a lowercase letter. Sometimes these letters also represent the length of the line segment, which is recorded as line segment AB or line segment BA, line segment a. where AB represents any two points on the straight line.

8. The difference between straight lines, rays, and line segments: Straight lines have no distance. Rays have no distance either. Because straight lines have no endpoints, rays have only one endpoint and can be extended indefinitely.

9. Angle: The figure composed of two non-overlapping rays with common endpoints is called an angle. This common endpoint is called the vertex of the angle, and these two rays are called the two sides of the angle.

The figure formed by a ray rotating from one position to another around its endpoint is called an angle. The endpoint of the rotated ray is called the vertex of the angle, the ray at the starting position is called the initial side of the angle, and the ray at the ending position is called the terminal side of the angle.

10. Static definition of angle: The figure composed of two non-overlapping rays with common endpoints is called an angle. This common endpoint is called the vertex of the angle, and these two rays are called the two sides of the angle.

11. Dynamic definition of angle: The figure formed by a ray rotating from one position to another around its endpoint is called an angle. The endpoint of the rotated ray is called the vertex of the angle, the ray at the starting position is called the starting side of the angle, and the ray at the ending position is called the terminal side of the angle

12. Symbol of angle: Symbol of angle: ∠

13. Types of angles: The size of the angle has nothing to do with the length of the sides; the size of the angle is determined by the degree to which the two sides of the angle are spread out. The greater the spread, the larger the angle. On the contrary, the spread is The smaller the , the smaller the angle. In dynamic definition, it depends on the direction and angle of rotation. Angle can be divided into 10 types: acute angle, right angle, obtuse angle, straight angle, circumferential angle, negative angle, positive angle, superior angle, inferior angle, and zero angle. The system of measuring angles in degrees, minutes, and seconds is called the angle system. In addition, there are also mil system, radian system, etc.

Acute angle: An angle greater than 0° and less than 90° is called an acute angle.

Right angle: An angle equal to 90° is called a right angle.

Ottagonal angle: An angle greater than 90° and less than 180° is called an obtuse angle.

Right angle: An angle equal to 180° is called a straight angle.

Superior angle: greater than 180° and less than 360° is called superior angle.

Minor angles: Greater than 0° and less than 180° are called minor angles. Acute angles, right angles and obtuse angles are all minor angles.

Peripheral angle: An angle equal to 360° is called a circumferential angle.

Negative angle: An angle formed by rotating clockwise is called a negative angle.

Positive angle: The angle rotated counterclockwise is a positive angle.

0 angle: an angle equal to zero degrees.

Supplementary angles and supplementary angles: If the sum of two angles is 90°, then the two angles are supplementary angles. If the sum of the two angles is 180°, then the two angles are supplementary angles. The supplementary angles of a congruent angle are equal, and the supplementary angles of a congruent angle are equal.

Opposite vertex angles: After two straight lines intersect, there is only one common vertex and the two sides of the two angles are opposite extensions of each other. Such two angles are called mutually opposite vertex angles. Two straight lines intersect to form two pairs of opposite angles. Two angles that are opposite to each other are equal.

There are also many kinds of angular relationships, such as interior angles, congruent angles, and interior angles on the same side. Among three lines and eight angles, they are mainly used to judge parallelism!

14 .Classification of geometric figures

***1*** Three-dimensional geometric figures can be divided into the following categories:

The first category: cylinder;

Including : cylinder and prism. Prisms can be divided into right prisms and oblique prisms. Prisms can be divided into triangular prisms, four prisms and N prisms according to the number of sides on the base;

The volume of a prism is uniformly equal to the area of ??the base Multiply by the height, that is, V=SH,

The second category: cone;

Includes: cone and pyramid, the pyramid is divided into three pyramids, four pyramids and N pyramids;

The volume of a pyramid is uniformly V=SH/3,

The third category: sphere;

This category only includes spheres, a geometric body,

The volume formula V=4πR3/3,

Other uncommon categories: circular cone, prism, spherical crown, etc. are rarely encountered.

Most geometries are composed of these geometries.

***2***How ??to classify plane geometric figures

a. Circles

b. Polygons: Triangles*** are divided into general triangles. Right triangle, isosceles triangle, equilateral triangle***, quadrilateral*** are divided into irregular quadrilateral, body shape, parallelogram, parallelogram is divided into: rectangle, rhombus, square***, pentagon, six...

Note: A square is both a rectangle and a rhombus

There are also many kinds of angle relationships, such as internal offset angles, congruent angles, and internal angles on the same side. ***Three lines and octagons are mainly used for Judging parallels***! Mathematics geometry review plan for the first volume of junior high school

1. Goals and requirements

1. Be able to abstract geometric figures from real objects and correctly distinguish three-dimensional figures and plane graphics; be able to transform some three-dimensional graphics problems into plane graphics for research and processing, and explore the relationship between plane graphics and three-dimensional graphics.

2. Experience exploring the relationship between two-dimensional graphics and three-dimensional graphics, develop spatial concepts, cultivate and improve the ability of observation, analysis, abstraction, and generalization, cultivate hands-on ability, experience the process of problem-solving, and improve the ability to solve problems. problem ability.

3. Actively participate in the teaching process, form a conscious and serious learning attitude, cultivate the spirit of daring to face learning difficulties, and feel the beauty of geometric figures; advocate independent learning and group cooperation spirit, and think independently Basically, students can benefit from group communication, correctly evaluate the learning process, and understand the importance of cooperative learning.

2. Knowledge Framework

3. Key Points

The key point is to abstract geometric figures from real objects and convert three-dimensional figures into plane figures;

Correctly determine whether the surface surrounding a three-dimensional figure is a plane or a curved surface, and exploring the relationship between points, lines, surfaces, and bodies is the key;

Draw a line segment equal to a known line segment, and compare the two The length of a line segment is one important point. In real situations, understanding the properties of a line segment "between two points, the shortest line segment" is another important point.

4. Difficulties

The transformation between three-dimensional graphics and plane graphics is a difficult point;

Explore the graphics formed after the movement changes of points, lines, surfaces and bodies It is a difficult point;

The ruler and compass drawing method of drawing a line segment equal to a known line segment, and correctly comparing the length of two line segments is a difficult point.

Methods for reviewing mathematics in the first year of junior high school

1. Pay attention to preview and guide self-study.

I personally think that previewing plays a relatively important role in junior high school, but generally does not pay much attention to it in elementary school. Therefore, most students in the first grade of junior high school will not preview, even if they have previewed , just read the text from beginning to end. When guiding students to preview, students should be required to do the following: rough reading, first briefly browse the relevant content of the textbook, and master the overview of the knowledge in this section. Second, read carefully, read, experience, and think about important concepts, formulas, rules, and theorems repeatedly, pay attention to the formation process of knowledge, mark difficult-to-understand concepts, and ask more "why" so that you can listen to the lecture with questions. The method can be class preview or unit preview. Before pre-study, the teacher first arranges the pre-study outline so that students can have a clear target. Listen to the teacher with your own questions in class, so that you can study with purpose and increase the effective time in class.

2. Listen carefully and take notes

Listening in class is very important. Listening carefully can get twice the result with half the effort. Since you have fully reviewed before class and there are still things you don’t understand about this lesson, then during the teacher’s lecture, watch how the teacher explains this knowledge point and compare it with your own obstacles in the preview process.

You should also listen carefully to the knowledge points that you have already understood, deepen your memory, see what the teacher has to offer, and pay more attention to what the teacher emphasizes. First-year junior high school students generally do not take notes properly. Students usually copy whatever the teacher writes on the blackboard, often using "note" instead of "listen" and "think". Although some notes are remembered completely, they have little effect. Therefore, when taking notes, pay attention to: take notes and listen to the lecture, and grasp the timing of recording; note key points, questions, ideas and methods for solving problems; note summaries, and write down after-class reflection questions. The purpose of taking notes is to better summarize and review. Do not blindly copy the teacher’s writing on the blackboard in class.

3. Review first and then do homework

First of all, we should establish a correct concept of homework. Do not complete homework for the sake of completing homework. Homework is for students to better master knowledge and let teachers understand students' problems. When many students do homework, they usually do it as soon as they pick up the questions. Once they encounter difficulties, they go back to the book and check their notes. This is a bad habit. The first step in doing homework should be to review the relevant knowledge. When reviewing, you can use the method of "watching movies" to search in your mind for the knowledge explained by the teacher in class, and try to recall the knowledge you have learned. If you really can't recall it, open the textbook again.

Or read and compare notes. In this way, you can review the knowledge you have learned and do your homework after you have a clear idea. After completing the problem, you should read it carefully from beginning to end to check whether the steps and ideas for solving the problem are correct.

1. Summary of knowledge points of junior high school mathematics

2. Summary of knowledge points of compulsory examination of mathematics in the first grade of junior high school

3. Knowledge points of mathematics in the second volume of seventh-grade mathematics

p>

4. Summary of key knowledge points in the first volume of junior high school mathematics

5. Summary of key knowledge points in the first volume of junior high school mathematics: rational numbers