What is the relationship between line and surface in a cube?

1. If a straight line out of plane is parallel to a straight line in this plane, then this straight line is parallel to this plane (from line to line, the line is parallel to the plane).

2. If the straight line A is parallel to the plane, if the plane passing through A intersects with, the intersection line must be parallel to A. 。

(Lines are parallel, lines are parallel)

3. If two intersecting straight lines on one plane are parallel to the other plane, then the two planes are parallel.

(The straight line is parallel to the plane, and the plane is parallel)

4. If the plane is a ∑ plane, then any straight line is parallel (from plane to plane, straight lines are parallel).

5. If two intersecting straight lines on one plane are parallel to two straight lines on another plane, then the two planes are parallel (from line to line, planes are parallel).

6. If two parallel planes intersect with the third plane, their intersection lines are parallel (from face to face, the lines are parallel).

Line, line, vertical line, vertical plane, vertical plane.

7. If a straight line is perpendicular to two intersecting straight lines in a plane, the straight line and the plane are perpendicular to each other (from line to line, the line surface is perpendicular).

8. If the straight line L is perpendicular to the plane, then the straight line L is perpendicular to any straight line in the plane.

(From the surface of the line to the vertical line, the line is vertical)

9. If one plane intersects the perpendicular of another plane, then the two planes are perpendicular to each other.

(Vertical from line to face, vertical from face to face)

10. If two planes are perpendicular to each other, a straight line perpendicular to their intersection on one plane is perpendicular to the other plane. (From face to face, the straight line is vertical. )

Three vertical line theorems

The diagonal of the plane is perpendicular to the straight line in the plane.

The projection of the diagonal segment on the plane is perpendicular to the straight line.