Axiom 2 passes through three points that are not on a straight line, and there is only one plane. In other words: three points of a straight line determine a plane.
Axiom 3: If two non-coincident planes have a common point, then they have one and only one common straight line passing through the point.
Axiom 4: Transitivity of spatial parallel lines: Two lines parallel to the same line are parallel to each other.
Definition: If a straight line is perpendicular to any straight line in the plane, we say that the straight line and the plane are perpendicular to each other.
If a straight line is perpendicular to two intersecting straight lines on a plane, then the straight line is perpendicular to the plane.
Two straight lines perpendicular to the same plane are parallel.
"Define" a straight line parallel to a plane if it has no common point with the plane.
If a line out of the plane is parallel to a line in the plane, the line is parallel to the plane.
Property A straight line is parallel to a plane, so the intersection of any plane passing through this straight line and this plane is parallel to this straight line.
"Definition" If two planes have nothing in common, we say they are parallel.
"Judgment" If two intersecting straight lines in one plane are parallel to another plane, then the two planes are parallel.
Property If two parallel planes intersect the third plane at the same time, their intersection lines are parallel.
Two planes are defined as intersecting. If the dihedral angle they form is a straight dihedral angle, the two planes are said to be perpendicular to each other.
"Judgment" If one plane passes through the vertical line of another plane, then the two planes are perpendicular to each other.
If two attribute planes are perpendicular, the straight line perpendicular to the intersection in one plane is perpendicular to the other plane.
If the straight line of theorem 1 on a plane is perpendicular to the projection of a diagonal line on this plane, then it is also perpendicular to this diagonal line.
If a straight line of Theorem 2 in a plane is perpendicular to a diagonal of this plane, then it is also perpendicular to the projection of this diagonal.