What is the triple vertical theorem?

The triple perpendicular theorem refers to a straight line on a plane. If it is perpendicular to the projection of a diagonal line passing through this plane on this plane, then it is also perpendicular to this diagonal line.

Three perpendicular theorems are one of the important theorems in solid geometry. If a straight line in a plane is perpendicular to the projection of a diagonal line in this plane, it is also perpendicular to the diagonal line. The Three Verticality Theorem determines that the diagonal is perpendicular to the straight line in the plane through the vertical relationship between the projection of the diagonal in the plane and the straight line in the plane. Because it involves three straight lines perpendicular to the known straight lines on the plane, it is called the three vertical theorem.

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1, the triple vertical theorem describes the vertical relationship among PO (diagonal), AO (projection) and a (straight line).

2. A and PO can intersect or be different.

3. The essence of the three-sag theorem is the judgment theorem that a diagonal line in space is perpendicular to a straight line in the plane. The key to the application of the three-vertical theorem is to find the vertical line of the plane (datum). As for projection, it is determined by vertical feet and inclined feet, so it is the second type. Starting from the proof of triple plumb theorem, a program to prove a⊥b is obtained: one vertical line, two shot puts and three proofs. That is, the first one.

note:

The four lines in 1 theorem are all aimed at the same plane.

The key to applying the theorem is to find the reference frame of "datum plane"

Attachment: Jiangsu Province's "Teaching Requirements" stipulates that since the 20 1 1 college entrance examination, the "three perpendicular lines theorem" cannot be used as the basis for reasoning and argumentation, and should be proved.

The "Teaching Requirements" of Heilongjiang Province stipulates that since the 20 12 college entrance examination, the "three vertical theorems" cannot be used as the basis for reasoning and argumentation, and should be proved.