Determination theorem:

1.? Definition: a line is perpendicular to a plane if a line and any line in the plane are perpendicular.

2.? If a line is perpendicular to two intersecting lines in a plane, the lines are perpendicular.

3.? If one of two parallel lines is perpendicular to a plane, the other is also perpendicular to that plane.

4.? If a line is perpendicular to one of two parallel planes, it is also perpendicular to the other plane.

5.? If two planes are perpendicular, then a line perpendicular to the line of their intersection in one plane is perpendicular to the other plane.

6.? If two intersecting planes are both perpendicular to another plane, then the line of their intersection is perpendicular to the other plane.

Extension

Related Proofs:

1. Points Outside the Plane

Set the point P is an arbitrary point outside the plane α, find a straight line PQ so that PQ ⊥ α.

Operation:

1) Make a straight line l arbitrarily inside α, and make PA ⊥ l through P, with the vertical foot

In this case, if PA ⊥ α, then the required PQ has been made; if this is not the case,

② Make m ⊥ l in α through A.

3) Make PQ ⊥ m through P, and the vertical foot is Q. Then PQ is the required line.

Proof:

From the work, l ⊥ PA, l ⊥ QA

∵ PA ∩ QA = A

∴ l ⊥ plane PQA

∴ PQ ⊥ l

And PQ ⊥ m, and m ∩ l = A, m ?α, l?α

∴PQ ⊥ α

2, the point in the plane

2. p>

Set point P is any point in the plane α, to make a straight line PQ so that PQ ⊥ α.

Operation:

①Over a point A out of the plane as AB ⊥ α, see above.

②PQ∥AB through P, PQ is the desired line.

Proof:

From the property theorem 3, if AB ⊥ α, PQ ∥ AB, then PQ ⊥ α.