1. Geometric figures can be abstracted from objects, and three-dimensional figures and plane figures can be correctly distinguished; Some problems of three-dimensional graphics can be transformed into plane graphics for research and processing, and the relationship between plane graphics and three-dimensional graphics can be explored.

2. Explore the relationship between plane graphics and three-dimensional graphics, develop the concept of space, cultivate and improve the ability of observation, analysis, abstraction and generalization, cultivate the ability of hands-on operation, experience the problem-solving process and improve the problem-solving ability.

3. Actively participate in the process of teaching activities, form a conscious and serious learning attitude, cultivate the spirit of daring to face learning difficulties, and feel the beauty of geometric figures; Advocate the spirit of autonomous learning and group cooperation, benefit from group communication on the basis of independent thinking, correctly evaluate the learning process and realize the importance of cooperative learning.

Second, the knowledge framework.

Third, the key points

Abstracting geometric figures from objects and transforming three-dimensional figures into plane figures are the key points;

It is the key to correctly judge whether the closed surface in three-dimensional graphics is a plane or a surface, and to explore the relationship between points, lines, surfaces and bodies.

Drawing a line segment is equal to a known line segment, and comparing the lengths of two line segments is an important point. In practice, understanding the properties of line segments "the shortest line segment between two points" is another key point.

Fourth, difficulties.

The conversion between three-dimensional graphics and plane graphics is difficult;

It is difficult to explore the graphics formed after the movement changes of points, lines, surfaces and bodies;

It is difficult to compare the lengths of two line segments correctly in the ruler drawing method where the line segment is equal to the known line segment.

Verb (abbreviation of verb) summary of knowledge points and concepts

1. Geometry: Points, lines, surfaces and bodies can help people effectively describe the complex world. It's all called geometry. All kinds of figures abstracted from objects are collectively called geometric figures. Geometric figures with parts not in the same plane are called three-dimensional figures. Some geometric figures are all in the same plane, which is called plane figures. Although solid figure and plane figure are two different geometric figures, they are interrelated.

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 in space moving in the same or opposite direction. From the point of view of plane analytic geometry, a straight line on a plane is a graph represented by a binary linear equation in a plane rectangular coordinate system. To require the intersection of two straight lines, we only need to solve these two binary linear equations simultaneously. When simultaneous equations have no solution, two straight lines are parallel. When there are infinite solutions, two straight lines coincide; When there is only one solution, two straight lines intersect at one point. The angle between a straight line and the positive direction of the X axis (called the inclination angle of the straight line) or the tangent of the angle (called the slope of the straight line) is often used to indicate the inclination of the straight line on the plane (for the X axis).

4. Ray: In Euclidean geometry, the figure formed by a point on a straight line and its edge is called a ray or a semi-straight line.

5. Line segment: refers to a continuous or discontinuous figure composed of one or more different line elements, such as a real line segment or a two-point long line segment composed of "long stroke, short interval, point, short interval, point and short interval".

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

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

7. Endpoint: Two points on a straight line and the part between them are called line segments, and these two points are called the endpoints of line segments.

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

8. The difference between straight lines, rays and line segments: straight lines have no distance. Ray has no distance. Because a straight line has no end point, a ray has only one end point and can extend indefinitely.

9. Angle: A graph composed of two non-overlapping rays with a common endpoint 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 the rotation of light 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 edge of the angle, and the ray at the ending position is called the ending edge of the angle.

10. Static definition of angle: A graph composed of two non-coincident rays with a common endpoint 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.

Dynamic definition of 1 1. Angle: The graph formed by the rotation of light from one position to another around its endpoint is called angle. The endpoint of the rotated ray is called the vertex of the angle, the ray at the starting position is called the starting edge of the angle, and the ray at the ending position is called the ending edge of the angle.

12. Angle symbol: Angle symbol:

13. Type of angle: the size of the angle has nothing to do with the length of the side; The size of an angle depends on the degree to which both sides of the angle are open. The bigger the opening, the bigger the angle. Conversely, the smaller the opening, the smaller the angle. In dynamic definition, it depends on the direction and angle of rotation. Angles can be divided into acute angle, right angle, obtuse angle, right angle, rounded corner, negative angle, positive angle, upper angle, lower angle and 0 angle, which are 10 respectively. An angle measuring system in degrees, minutes and seconds is called an angle system. In addition, there are secret system, arc system and so on.

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.

Oblique angle: an angle greater than 90 and less than180 is called obtuse angle.

Boxer: An angle equal to 180 is called a boxer.

Excellent angle: more than180 and less than 360 is called excellent angle.

Bad angle: it is called bad angle when it is greater than 0 but less than 180. Acute angle, right angle and obtuse angle are all bad angles.

Fillet: An angle equal to 360 is called a fillet.

Negative angle: the angle formed by clockwise rotation is called negative angle.

Positive angle: the angle of counterclockwise rotation is positive angle.

Angle 0: An angle equal to zero.

Complementary angle and complementary angle: if the sum of two angles is 90, it is complementary angle, and if the sum of two angles is180, it is complementary angle. The complementary angles of equal angles are equal, and the complementary angles of equal angles are equal.

Inverse vertex angle: When two straight lines intersect, there is only one common vertex, and both sides of the two corners are opposite extension lines. These two angles are called antipodal angles. Two straight lines intersect to form two pairs of vertex angles. The two opposite angles are equal.

There are also many kinds of angle relationships, such as internal dislocation angle, congruent angle and internal angle of the same side (in the three-line octagon, it is mainly used to judge parallelism)!

14. Geometric classification

(1) solid geometry can be divided into the following categories:

The first category: cylinders;

Comprises a cylinder and a prism, wherein the prism can be divided into a straight prism and an oblique prism, and the prism can be divided into a triangular prism, a quadrangular prism and an N prism according to the number of sides of the bottom surface;

The volume of the prism is equal to the area of the bottom multiplied by the height, that is, V=SH,

The second category: cones;

Comprises a cone and a pyramid, wherein the pyramid is divided into a triangular pyramid, a quadrangular pyramid and an n-pyramid;

The pyramid volume is unified as V=SH/3,

The third category: sphere;

This classification contain only one geometric shape of a sphere,

The volume formula V=4R3/3,

Other uncommon classifications: frustum of a cone, pyramid, spherical cap, etc. Rarely touched.

Most geometric figures are composed of these geometric figures.

(2) How to classify plane geometry?

A. circle

B Polygons: triangles (divided into general triangles, right triangles, isosceles triangles and equilateral triangles), quadrangles (divided into irregular quadrangles, body shapes and parallelograms, and parallelograms are divided into rectangles, diamonds and squares), pentagons and hexagons.

Note: A square is both a rectangle and a diamond.