1, the straight lines of two * * * planes do not intersect. L 1∈a, l2∈a, l 1∩l2= empty set (definition, not commonly used).

2. Two lines parallel to the same line are parallel. L1/L2, l1/L3, and then l2//l3 (transfer mode).

3. Two straight lines perpendicular to the same plane are parallel. L 1⊥a,l2⊥a, then l1/L2.

4. Plane A and B intersect at l 1. If l2 is parallel to A or B, l 1 is parallel to l2. A∩b=l 1, l2//a, then l1/L2.

5. In analytic geometry, two straight lines are parallel if their direction vectors are parallel. (coordinate method)

2. Parallelism of lines and planes

1. If the line and the plane have no common point, the line is parallel to the plane. (definition)

2. A straight line out of the plane is parallel to a straight line in the plane, then the straight line is parallel to the plane. (most commonly used)

3. In analytic geometry, a straight line out of the plane is parallel to the plane if it is perpendicular to the normal vector of the plane. (coordinate method)

Third, the surfaces are parallel.

1. The two planes have nothing in common. (definition)

2. Two intersecting straight lines on the plane are parallel to the other straight line, so the two planes are parallel. (most commonly used)

3. Two planes perpendicular to the same straight line are parallel.

4. In analytic geometry, two planes are parallel if their normal vectors are parallel.

Fourth, the line is vertical.

1. The angle between two straight lines is 90 degrees (definition).

2. The plane in which a straight line is perpendicular to another straight line (most commonly used)

V. Vertical lines and planes

1. The angle between the straight line and the plane is 90 degrees.

2. The straight line is perpendicular to two intersecting straight lines on the plane (most commonly used)

Six, face to face vertical

1. The included angle between two intersecting planes is 90 degrees. (definition)

2. A straight line in one plane is perpendicular to another plane (most commonly used)

Note: There are some things that are not commonly used. In fact, there is no need to deliberately remember which proof. These are all equivalent and can be deduced from each other. The key is to exercise a kind of spatial imagination and keen observation of mathematical problems.