How to prove that two planes are perpendicular?

The method of proving that two planes are perpendicular is as follows:

First, the line is vertical.

If two planes are perpendicular to each other, a straight line perpendicular to their intersection on one plane is perpendicular to the other plane. As we all know, a straight line must be perpendicular to the intersection of two planes. If this straight line in one plane is not 90 degrees from the intersection, then it is not 90 degrees from another plane.

Second, the surface is vertical.

If two intersecting planes are perpendicular to the third plane, their intersection line is perpendicular to the third plane. The length of the common vertical line segment is unique, and the length of this common vertical line segment is called the distance between two parallel planes. Obviously, this distance is also equal to the length of the vertical section from any point on one plane to another plane.

The distance between two straight lines on different planes, the distance between a straight line parallel to a plane and a plane, and the distance between two parallel planes all boil down to the distance between two points.

Third, the vertical line is vertical.

If two planes are perpendicular to each other, the perpendicular of one plane is parallel to the other. It is axiomatic that three points not on the same straight line form a plane, so take any three points on the parallel line to form a plane (1, 2 points are on line A and 3 points are on line B).

Then it is proved that any fourth point on the parallel line (either on line A or line B) must belong to this plane. If the fourth point is on line A: the fourth point is on the same line as the other two points, then it must belong to this plane.

Vertical theorem and its generalization theorem;

I. Vertical Theorem

In plane geometry, if a straight line is perpendicular to any straight line on the plane, then this straight line is also perpendicular to the plane. This theorem is also called the vertical theorem.

Second, the generalization theorem of vertical theorem

The generalization theorem of vertical theorem means that if a straight line is perpendicular to any straight line on a plane in three-dimensional space, then the straight line is also perpendicular to the plane.

The generalized theorem of vertical theorem can also be used to describe some special geometric bodies, such as pyramids, prisms and truncated cones. These geometric bodies have a special property that all their faces are pyramid faces or prism faces, and all their edges are perpendicular to a plane.