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 one and only one common straight line passing through this point.

Axiom three

Passing through three points that are not on the same straight line has one and only one plane.

Inference 1

Through a straight line and a point outside this straight line, there is only one plane.

Inference 2

Passing through two intersecting lines, there is one and only one plane.

Inference 3

Passing through two parallel straight lines, there is only one plane.

Determination of plane intersection

If two planes have a common point, they are said to intersect.

Determination of parallelism of line and plane

A straight line out of the plane is parallel to a straight line in this plane, so this straight line is parallel to this plane.

Determination of plane parallelism 1

If two intersecting lines on one plane are parallel to the other plane, then the two planes are parallel.

Determination of plane parallelism II

Two planes perpendicular to the same line are parallel.

Properties of parallel lines and planes

A straight line is parallel to a plane, so any plane passing through this straight line is parallel to the intersection of this plane.

Property 1 of plane parallelism

If two parallel planes intersect the third plane at the same time, their intersection lines are parallel.

The second property of plane parallelism

If a straight line is in a plane, the plane parallel to this plane is parallel to this straight line.

Determination of vertical line and plane 1

A straight line is perpendicular to two intersecting straight lines on a plane, so this straight line is perpendicular to the plane.

Determination of vertical line and plane II

If a line is perpendicular to a plane, a line parallel to the line is perpendicular to the plane.

Determination of plane verticality

If one plane intersects the perpendicular of the other plane, the two planes are perpendicular.

Properties of vertical line and plane

Two straight lines perpendicular to the same plane are parallel.

The nature of vertical plane.

If two planes are perpendicular, a straight line perpendicular to the intersection in one plane is perpendicular to the other plane.