Structural characteristics of mathematical knowledge point 1, column, cone, table and ball

(1) prism:

Geometric features: the two bottom surfaces are congruent polygons with parallel corresponding sides; The lateral surface and diagonal surface are parallelograms; The sides are parallel and equal; The section parallel to the bottom surface is a polygon that is congruent with the bottom surface.

② Pyramid

Geometric features: the side and diagonal faces are triangles; The section parallel to the bottom surface is similar to the bottom surface, and its similarity ratio is equal to the square of the ratio of the distance from the vertex to the section to the height.

(3) Prism:

Geometric features: ① The upper and lower bottom surfaces are similar parallel polygons; ② The side is trapezoidal; ③ The sides intersect with the vertices of the original pyramid.

(4) Cylinder: Definition: It is formed by taking a straight line on one side of a rectangle as the axis and rotating the other three sides.

Geometric features: ① The bottom is an congruent circle; ② The bus is parallel to the shaft; ③ The axis is perpendicular to the radius of the bottom circle; ④ The side development diagram is a rectangle.

(5) Cone: Definition: A Zhou Suocheng is rotated with a right-angled side of a right-angled triangle as the rotation axis.

Geometric features: ① the bottom is round; (2) The generatrix intersects with the apex of the cone; ③ The side spread diagram is a fan.

(6) frustum of a cone: Definition: Take the vertical line of the right-angled trapezoid and the waist of the bottom as the rotation axis, and use Zhou Suocheng to rotate.

Geometric features: ① The upper and lower bottom surfaces are two circles; (2) The side generatrix intersects with the vertex of the original cone; (3) The side development diagram is an arch.

(7) Sphere: Definition: The geometric features of the geometric body formed by taking the straight line with semicircle diameter as the rotation axis and the semicircle surface rotating once: ① the cross section of the sphere is circular; ② The distance from any point on the sphere to the center of the sphere is equal to the radius.

Knowledge points of mathematics II. Three views of space geometry

Define three views: front view (light is projected from the front of the geometry to the back); Side view (from left to right) and top view (from top to bottom)

Note: the front view reflects the height and length of the object; The top view reflects the length and width of the object; The side view reflects the height and width of the object.

Mathematical knowledge points 3. Intuition of space geometry-oblique two-dimensional drawing method

The characteristics of oblique bisection method are as follows: ① The line segment originally parallel to the X axis is still parallel to X, and its length remains unchanged;

② The line segment originally parallel to the Y axis is still parallel to Y, and its length is half of the original.

Knowledge points of solid geometry in senior high school mathematics II

First of all, the plane

It is usually represented by a parallelogram.

Planes are often represented by Greek letters α, β, γ … or Latin letters M, N, P, and can also be represented by two opposite vertex letters of a parallelogram, such as plane AC.

In solid geometry, uppercase letters A, B, C, … represent points, lowercase letters A, B, c…l, M, n… represent straight lines, and straight lines and planes are regarded as a collection of points, so we can use symbols in set theory to express the relationship between them, for example:

A)a∈l- point a is on a straight line l; An α point A is not in the plane α;

B)lα— The straight line l is in the plane α;

C) α-straight line A is not in plane α;

D) l ∩ m = a-straight line l and straight line m intersect at point a;

E) α ∩ l = a —— Plane α intersects with straight line L at point A;

F)α∩β= L- Plane α and Plane β intersect in a straight line L. 。

Second, the basic nature of the aircraft

Axiom 1 If two points on a straight line are on the same plane, then all points on this straight line are on this plane.

Axiom 2 If two planes have a common point, then they have only one common straight line passing through this point.

Axiom 3 passes through three points that are not on the same straight line, and there is only one plane.

According to the above axioms, the following inferences can be drawn.

Inference 1 There is only one plane through a straight line and a point outside this straight line.

Inference 2 passes through two intersecting straight lines, and there is only one plane.

Inference 3 passes through two parallel straight lines, and there is only one plane.

Axiom 4 Two lines parallel to the same line are parallel to each other.