2. There is only one plane when crossing three points that are not on the same straight line. (There is no * * * line, three-point given surface)
Inference:
The (1) plane can be determined by a straight line and a point outside the straight line.
(2) The plane can be determined by two intersecting straight lines.
(3) The plane can be determined by two parallel straight lines.
3. If two non-coincident planes have a common point, then they only have a common straight line passing through the point.
4. Two lines parallel to the same line are parallel.
5. Equiangular theorem;
In space, if the two sides of two angles are parallel, then the two angles are equal or complementary;
If the directions of two angles are the same, then the two angles are equal;
Two angles are complementary if their directions are opposite.
6. Theorem for judging that a straight line is parallel to a plane: (If a straight line is parallel to a plane, the straight line is parallel to the plane)
If the straight line out of plane is parallel to the straight line in plane, then the straight line in plane is parallel to the plane.
7. Judgment theorem of plane parallelism: (If a straight line is parallel to a plane, the plane is parallel)
If two intersecting lines in one plane are parallel to the other plane, the two planes are parallel.
8. If the straight line is parallel to the plane, then the plane intersecting the straight line intersects the original plane, and the straight line is parallel to the intersection line.
9. If two planes intersect with the third plane at the same time, their intersection lines are parallel.
10. If a straight line is perpendicular to all the straight lines in the plane, then the straight line is perpendicular to the plane.
1 1. If a plane passes through a straight line of another plane, then the two planes are perpendicular.
12. If the dihedral angle formed by two planes is 90, the two planes are vertical.
13. If two straight lines are perpendicular to a plane, then the two straight lines are parallel.
14. If two planes are perpendicular, then the straight line passing through one plane and perpendicular to their intersection line is perpendicular to the other plane.
15. If a straight line in the plane is perpendicular to the projection of the diagonal in the plane, it is perpendicular to the diagonal.
16. If a line in the plane is perpendicular to the diagonal of the plane, then it is perpendicular to the projection of the diagonal in the plane.