Three perpendiculars theorem and its converse theorem

Three Perpendicular Line Theorem Definition: If a straight line in a plane is perpendicular to the projection of an oblique line in this plane in this plane, then it is also perpendicular to this oblique line. The converse of the three perpendicular theorem: If a straight line in a plane is perpendicular to an oblique line on the plane, then it is also perpendicular to the projection of the oblique line on the plane.

The details are as follows:

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

2. a and PO can intersect or be in different planes.

3. The essence of the three perpendicular theorem is the determination theorem that an oblique line on the plane is perpendicular to a straight line in the plane. About The key to the application of the three-perpendicular determination is to find the perpendicular to the plane (datum plane). As for the projection, it is determined by the vertical foot and the oblique foot, so it is second.?

From The proof of the three perpendicular theorem is a procedure to prove a⊥b: one perpendicular, two projections, three proofs. That is, first, find the plane (datum plane) and the plane perpendicular. Second, find the projective line. At this time, a, b It becomes a straight line and an oblique line on the plane. Third, prove that the projection line is perpendicular to the straight line a, so it can be concluded that a and b are perpendicular.