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MindMap Gallery Preliminary solid geometry

Preliminary solid geometry

This is a preliminary mind map about solid geometry, including a cylinder: two surfaces are parallel and congruent, and the intersection lines of each remaining two adjacent surfaces are parallel to each other; in addition, the cylinder can also be divided into Right cylinder, oblique cylinder.

Edited at 2022-05-03 09:55:54

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Preliminary solid geometry

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Outline

solid geometry

Common solid geometric figures

prism

pyramid

ball

cylinder

Round table

cone

volume formula Prism/Cone: Sh/3 Ball: 4πr³/3 Edge/column: V=Sh Edge/ground: V=h(S₁ S₂ √s₁s₂)/3

Classification

cylinder

concept

There are two faces that are parallel and congruent to each other, and the intersection lines of each remaining two adjacent faces are parallel to each other; in addition, the cylinder can also be divided into a straight cylinder and an oblique cylinder.

cone

concept

Bounded by the surface formed by a circular or other closed planar base and line segments connecting points on the boundary of the base to a common vertex.

body of revolution

concept

The surface formed by the rotation of a plane curve around a fixed line in the plane where it is located is called a surface of revolution; the fixed line is called the axis of the body of revolution; the geometry surrounded by a closed surface of revolution is called a body of revolution.

Sectional body

concept

Section refers to cutting a geometric body with a plane, and the resulting geometric figure is called a cross-section body.

Relationship transformation diagram

Positional relationship

between lines

Coplanar

parallel

Line ① // Line ②

intersect

Line ② intersects line ③ at point A' (including perpendicular: line ①⊥ line ③)

Different side

Contains vertical: line ①⊥ line ④

between lines and surfaces

parallel

Line ② // Surface ①

intersect

Line ①∩ surface ③=D'

Include

Line ① is included in surface ①

between faces

parallel

Noodle ①//Noodle ②

intersect

Face①∩face③=DD' (including vertical: face①⊥face③)

formula

space angle

Angle formed by straight lines with different faces

scope

θ∈（0°,90°]

concept

If two straight lines are drawn through any point in space and are parallel to two straight lines in different planes, the acute angle (or right angle) they form is the angle formed by the straight lines in different planes.

Angle between a straight line and a plane

scope

θ∈[0°,90°]

concept

Draw a perpendicular to the plane through a point on a straight line that is not parallel to the plane. The line connecting the intersection point of this straight line with the plane and the intersection point of the original straight line and the plane is formed by the original straight line (the supplementary angle of the angle between this line and the original straight line) ) is the line-surface angle.

dihedral angle

scope

θ∈[0°,180°]

concept

The figure formed by two half-planes starting from a straight line is called a dihedral angle. The straight line is called the edge of the dihedral angle. The two half-planes are called the faces of the dihedral angle.

regular prism A regular prism is a prism whose side edges are perpendicular to the base and whose base is a regular polygon.

right prism A prism whose side edges are perpendicular to the base is called a right prism. When drawing a straight prism, the side edges should be drawn perpendicular to the base.

oblique prism A prism whose side edges are not perpendicular to the base is called an oblique prism. When drawing an oblique prism, the side edges are generally drawn so that they are not perpendicular to the base.

Face to face vertical

vertical line

Face to face parallel

Lines and planes are parallel

Lines are parallel

formula Lines are parallel: line ① // line ②, line AB // line ② → line ① // line AB Line vertical: line ①⊥ line ③, line ① // line ② → line ②⊥ line ③ Lines and surfaces are parallel: Line ① // Line ②, line ① is included in surface ① → Line ② // Surface ① The line and plane are vertical: line B'C'⊥line②, line B'C'⊥line④, line②∩line④=B', line④ is included in face②, line② is included in face②→line B'C' ⊥face② Surfaces are parallel: line ②//surface ①, line ④//surface ①, line ②∩ line ④=B', line ④ is included in surface ②, line ② is included in surface ② → surface ②//surface ① Surface perpendicular: line ③⊥ surface ②, line ③ is included in surface ③ → surface ③⊥ surface ②