The method of proving that a line and a plane are perpendicular is as follows:

1. Determination theorem of a line and a plane being perpendicular

A straight line is perpendicular to two intersecting straight lines in a plane

2. The property of surface perpendicularity

If two planes are perpendicular, then a straight line perpendicular to the intersection line on one surface must be perpendicular to the other plane

3. Lines and surfaces are perpendicular Properties

If one of the two parallel lines is perpendicular to the plane, the other is also perpendicular to the plane

4. Properties of parallel surfaces

One line is perpendicular to two One of the parallel planes must be perpendicular to the other plane

5. Definition method

A straight line is perpendicular to any straight line in the plane

It can be known from Property Theorem 2 , through a point in space (whether on a known plane or not), there is and is only one straight line perpendicular to the plane. Let's discuss how to make this unique straight line.

The point is outside the plane

Suppose point P is any point outside the plane α, find a straight line FPQ to make PQl a.

How to do it:

① Draw a straight line 1 in α, and pass it through P to make 1 on PA, and the vertical foot is A.

At this time, if PAl a, the required PQ has been made; if not,

② pass A within α and do m on 1.

3 Through P, draw m on PQ, and the vertical foot is Q, then PQ is the desired straight line.