(1) Basis for judging straight lines in the plane
(2) the method of judging whether a point is in a plane.
Axiom 2: If two planes have a common point, there are other common points, and the set of these common points is a straight line.
(1) Basis for judging the intersection of two planes
(2) judging that there are a plurality of points on the intersection line of two intersecting planes
Axiom 3: After passing through three points that are not on a straight line, there is one and only one plane. (1) Determine the basis of the plane
(2) The basis of judgment is * * *
Inference 1: Through a straight line and a point outside this straight line, there is one and only one plane. (1) Basis for judging several straight lines * * * planes
(2) the basis for judging the coincidence of several planes
(3) The basis for judging that geometric figures are plane figures.
Inference 2: Through two intersecting straight lines, there is one and only one plane.
Inference 3: After passing through two parallel lines, there is one and only one plane.
Solid geometric straight lines and planes
Two straight lines in space are parallel to each other.
Axiom 4: Two lines parallel to the same line are parallel to each other.
Equiangular Theorem: If two sides of one angle are parallel and in the same direction as two sides of another angle, then the two angles are equal.
Heteroplane straight line
Relationship between straight line and spatial plane position
(1) The straight line is in the plane-there are countless things in common.
(2) A straight line intersects a plane-there is only one common point.
(3) The straight line is parallel to the plane-there is nothing in common.
Solid geometric straight lines and planes
The angle between a straight line and a plane.
The acute angle formed by the oblique line of (1) plane and its projection on the plane is called the angle formed by this oblique line and the plane.
(2) A straight line is perpendicular to the plane, and the angle formed by this straight line and the plane is defined as a right angle.
(3) The straight line is parallel to the plane, or in the plane, and its angle with the plane is defined as 00.
A straight line in the plane of the Three Verticality Theorem is perpendicular to the diagonal of the plane if it is perpendicular to the projection of the plane.
The projection of a straight line perpendicular to the diagonal in the plane of the inverse theorem of three perpendicular lines.
Measurement of parallelism between two planes in space
nature
(1) If two intersecting lines in one plane are parallel to the other plane, the two planes are parallel.
(2) Two planes perpendicular to the same straight line are parallel.
(1) Two planes are parallel, and the straight line in one plane must be parallel to the other plane.
(2) If two parallel planes intersect with the third plane at the same time, their intersection lines are parallel.
(3) The straight line is perpendicular to one of the two parallel planes, and it is also perpendicular to the other plane.
Dihedral angle of two intersecting planes: the figure formed by two half planes starting from a straight line is called dihedral angle, this straight line is called dihedral angle line, and these two half planes are called dihedral angle planes.
Plane angle of dihedral angle: The plane angle of dihedral angle is defined as two rays with either side of dihedral angle as the endpoint and the other vertical side in two planes.
A dihedral angle whose plane angle is a right angle is called a straight dihedral angle.
Biplane vertical judgment
nature
If one plane passes through the perpendicular of the other plane, then the two planes are perpendicular to each other.
(1) If two planes are perpendicular, the line perpendicular to their intersection in one plane is perpendicular to the other plane.
(2) If the two planes are perpendicular, a straight line passing through a point in the first plane and perpendicular to the second plane is in the first plane.
Solid geometry polyhedron, prism, pyramid
polyhedron
Defining a geometry surrounded by several polygons is called a polyhedron.
Prism oblique prism: a prism whose side is not perpendicular to the bottom.
Straight prism: A prism whose side is perpendicular to the bottom.
Regular prism: a regular prism with a regular polygon at the bottom.
Pyramid regular pyramid: If the bottom of a pyramid is a regular polygon and the projection of the vertex on the bottom is the center of the bottom, such a pyramid is called a regular pyramid.
ball
A point set whose distance to a point is equal to or less than a fixed length.
euler theorem
There is a relationship between the number of vertices v, the number of edges e and the number of faces f of a simple polyhedron: V+F-E=2.