Property Theorem of Vertical Line and Plane 1: If a straight line is perpendicular to a plane, then it is perpendicular to all the straight lines in the plane.
Theorem 2: Through a point in space, there is one and only one straight line perpendicular to the known plane.
Theorem 3: If one of two parallel lines is perpendicular to a plane, then the other line is also perpendicular to the plane.
Theorem 4: Two straight lines perpendicular to the same plane are parallel.
Judgement theorem of perpendicularity between line and plane: If a straight line is perpendicular to two intersecting straight lines in a plane, then this straight line is perpendicular to this plane.
If the straight line L is perpendicular to the two intersecting straight lines AB and CD on the surface S, then l⊥ surface S
Assuming that L is not perpendicular to the plane S, it is either L∑S or oblique S and the included angle is not equal to 90.
When l∑S, then l can't be perpendicular to AB and CD at the same time. This is because when l⊥AB, if a plane R and S arbitrarily intersect M after L, then m∨l can be known from the parallel nature of lines and planes.
∴m⊥AB
Another ∵l⊥CD
∴m⊥CD
∴AB∥CD, which contradicts the known conditions.
When L and S intersect obliquely, if the intersection point is a straight line n⊥l in S, then N and L form a new plane T, and T and S intersect obliquely (if T⊥S, then N is the intersection of two planes. From the vertical nature of the surface, we can know that l⊥S is contradictory L oblique S)
∵l⊥AB
∴AB∥n
∵l⊥CD
∴CD∥n
∴AB∥CD, which contradicts the known conditions.
In a word, l⊥S