Structural characteristics of common space geometry in compulsory mathematics of senior one and compulsory mathematics of senior two.

(1) prism, pyramid, prism and polyhedron

A prism is a geometric body surrounded by faces satisfying the following three conditions: ① There are two faces parallel to each other; (2) Other faces are quadrilateral; ③ The public sides of every two adjacent quadrangles are parallel to each other; Prisms can be divided into three prisms, four prisms and five prisms according to the number of sides of the bottom. Prism properties: ① All sides of a prism are parallelograms and all sides are equal; (2) The two bottom surfaces of the prism and the sections parallel to the bottom surfaces are congruent polygons with parallel corresponding sides.

③ The cross sections of two non-adjacent sides of a prism are parallelograms.

A pyramid is a geometric body surrounded by a triangle, the bottom of which is a polygon, and the other side is a common vertex. Pyramids have the following properties: ① The bottom is polygonal; ② The edge is a triangle with the vertex of the pyramid as the common point; ③ The cross sections parallel to the bottom surface and the bottom surface are similar polygons, and the similarity ratio is equal to the ratio of the distance from the vertex to the cross section and the distance from the vertex to the bottom surface. The ratio of the cross-sectional area to the bottom surface area is equal to the square of the above similarity ratio.

A pyramid is the part between the cross section and the bottom surface after the pyramid is cut by a plane parallel to the bottom surface. According to the definition of pyramid, all the extension lines of the sides intersect at one point, and then the pyramid is restored.

A polyhedron is a geometric body surrounded by several polygons. A polyhedron with several faces is called a polyhedron. For example, a triangular pyramid is a tetrahedron.

(2) Cylinders, cones, frustums and spheres

The geometric bodies formed by rotating one side of a rectangle, the right side of a right triangle, the right trapezoid perpendicular to the straight line of the waist at the bottom, and the semicircle with the straight line of its diameter as the rotation axis are called cylinders, cones, frustums and spheres.

The properties of cylinder, cone and frustum are as follows: ① The sections parallel to the bottom are all circles; (2) The cross sections passing through the shaft are congruent rectangles, isosceles triangles and isosceles trapezoid respectively; (3) When the upper bottom surface and the lower bottom surface of the frustum are at the same time, a cylinder can be obtained; When the upper and lower surfaces of frustums are reduced to a point, a cone can be obtained.

This is part of the teaching plan I wrote for the tutoring students before. If it helps, please adopt it. If you don't understand, please ask.