What is the three perpendicular theorem?

The three perpendicular theorem refers to a straight line in a plane that is perpendicular to the projection of a diagonal line passing through the plane on the plane, then it is also perpendicular to the diagonal line.

The three perpendicular theorem is one of the important theorems of solid geometry. The three perpendicular theorem determines that the oblique line is perpendicular to a straight line in the plane through the vertical relationship between the projection of the plane oblique line and a straight line in the plane. Since The theorem involves three straight lines that are perpendicular to known straight lines in the plane, so it is called the three perpendicular theorem.

The three perpendicular theorem describes the vertical relationship between PO (oblique line), AO (projection), and a (straight line). a and PO can intersect or have different sides. The essence of the three perpendicular theorem is the determination theorem that a diagonal line in space is perpendicular to a straight line in a plane. Regarding the application of the three perpendicular theorem, the key is to find the perpendicular to the plane (datum).

The projection is determined by the vertical and oblique feet, so it is secondary. From the proof of the three perpendicular theorem, we get a procedure to prove a⊥b: one perpendicular, two radii, and three proofs. That is, the first finding plane (datum plane) and the second finding line perpendicular to the plane find the projection line. At this time, a and b become a straight line and an oblique line on the plane. Third, it is proved that the projective line is perpendicular to the straight line a, so that a and b are perpendicular.

Explanation

1. Lines are vertical (plane problem)? Lines are oblique and vertical (space problem).

2. Methods to prove that lines are perpendicular: definition method; line perpendicularity determination theorem; three perpendicular lines theorem.

3. The three perpendicular theorem describes the vertical relationship between PO (oblique line), AO (projection), and a (straight line).

4. Line a and PO can intersect or be in different planes.

5. The essence of the three perpendicular theorem is the determination theorem that a diagonal line on the plane is perpendicular to a straight line in the plane.

6. It can be used to solve problems such as angles formed by out-of-plane straight lines and plane angles of dihedral angles.