1. Line and line are parallel to 1, and two straight lines with * * * plane have no intersection. L 1∈a, l2∈a, l 1∩l2= empty set (definition, not commonly used). 2. Two lines parallel to the same line are parallel. L6545 and then l2//l3 (transfer mode) 3. Two straight lines perpendicular to the same plane are parallel. L 1⊥a,l2⊥a, and then l1/l24. Planes a and b intersect at l 1. If l2 is parallel to A or B, L65438. Two straight lines are parallel if their direction vectors are parallel. (coordinate method) 2. Parallelism of line and plane 1. If a straight line and a plane have no common point, then it is parallel to the plane. (definition) 2. The straight line out of the plane is parallel to the straight line in the plane, and it is parallel to the plane. (most commonly used) 3. In analytic geometry, then the straight line is parallel to the plane. (coordinate method) 3. This plane is parallel to the plane 1. There is nothing in common between these two planes. (definition) 2. Two intersecting lines on a plane are parallel to the other line, so the two planes are parallel. (most commonly used) 3. Two planes perpendicular to the same line are parallel. 4. In analytic geometry, if two planes are parallel, then they are parallel. Fourth, the straight line is perpendicular to 1. The angle between two straight lines is 90 degrees (defined). Second, a straight line is perpendicular to the plane of another straight line (most commonly used). Fifth, the straight line is perpendicular to 1. The angle between the straight line and the plane is 90 degrees. Second, the straight line is perpendicular to two intersecting straight lines in the plane (most commonly used). Sixth, the plane is vertical. The angle between two intersecting planes is 90 degrees. (definition) 2. A straight line on one plane is perpendicular to another plane (most commonly used). Note: There are some uncommon ones not listed. There is no need to remember which one to prove. 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.