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

Inference of surface vertical judgment theorem;

Inference 1: If the perpendicular of one plane is parallel to the other plane, then the two planes are perpendicular to each other.

Inference 2: If the perpendicular lines of two planes are perpendicular to each other, then the two planes are perpendicular to each other.

Definition of surface verticality: If the dihedral angle of two planes is a straight dihedral angle (the plane angle is the dihedral angle of a right angle), then the two planes are perpendicular to each other.

Theorem of vertical property of plane;

Theorem 1: If two planes are perpendicular to each other, a straight line perpendicular to their intersection on one plane is perpendicular to the other plane.

Theorem 2: If two planes are perpendicular to each other, then a straight line perpendicular to the second plane through a point in the first plane is in the first plane.

Theorem 3: If two intersecting planes are perpendicular to the third plane, then their intersection line is perpendicular to the third plane.

Inference: The intersection of three pairwise vertical planes is pairwise vertical.

Theorem 4: If two planes are perpendicular to each other, the perpendicular of one plane is parallel to the other. (The decision theorem deduces the inverse theorem of 1

Inference: If two planes are perpendicular to each other, then two perpendicular lines perpendicular to these two planes are also perpendicular to each other. (Decision Theorem Inference 2 Inverse Theorem).

Face to face vertical:

The perpendicularity theorem of surface is one of the classical geometric theorems in mathematics, one of the basic theorems in Euclidean geometry and one of the widely used geometric theorems. The surface vertical theorem is a relatively basic theorem in junior high school mathematics, but it is widely used in real life.

For example, in building engineering, designers need to ensure the vertical relationship between walls, floors, ceilings and other components to ensure the stability and aesthetics of the building. In addition, in computer graphics, the surface verticality theorem is also widely used in 3D modeling and rendering to ensure the authenticity and visual effect of graphics.

The perpendicularity theorem of surface is a very important geometric theorem in mathematics, which is widely used in real life. By studying and understanding this theorem, we can better apply mathematical knowledge to solve practical problems and improve our mathematical literacy and practical ability.