Basic fact 1: There is only one plane through three points that are not on a straight line. (Three points that are not collinear determine a plane)

Basic fact 2: If two points on a line lie in a plane, then the line lies in this plane.

Basic fact 3: If two non-overlapping planes have a common point, then they have one and only one common straight line passing through that point.

Corollary 1: There is and is only one plane passing through a straight line and a point outside the straight line.

Corollary 2: There is one and only one plane passing through two intersecting straight lines.

Corollary 3: There is only one plane passing through two parallel straight lines.

Straight lines and straight lines

straight lines and planes

Plane and Plane

Basic Fact 4: Two straight lines parallel to the same straight line are parallel.

Theorem: If the two sides of two angles in space are parallel, then the two angles are equal or complementary.

Theorem: If a straight line outside a plane is parallel to a straight line in this plane, then the straight line is parallel to this plane.

Theorem: A straight line is parallel to a plane. If a plane passing through the straight line intersects the plane, then the straight line is parallel to the intersection line.

Theorem: If two intersecting lines in one plane are parallel to another plane, then the two planes are parallel.

Theorem: Two planes are parallel. If another plane intersects these two planes, then the two intersection lines are parallel.

The definition of, the distance from line to line, the angle between straight lines with different planes

Definition, distance from line to surface, vertical line, vertical surface, vertical foot, vertical line segment, angle between straight line and plane

There is only one straight line perpendicular to a known plane through a point.

Theorem: If a straight line is perpendicular to two intersecting straight lines in a plane, then the straight line is perpendicular to the plane.

Theorem: Two straight lines perpendicular to the same plane are parallel.

Definition of, distance from face to face, edge of dihedral angle, face of dihedral angle, square angle of dihedral angle

Theorem: If one plane passes through the perpendicular to another plane, then the two planes are perpendicular

Theorem: Two planes are perpendicular. If there is a straight line in one plane perpendicular to the intersection of the two planes, then this straight line is perpendicular to the other plane.

(on y-axis)