1. Parallel lines (lines are parallel)

Judgment theorem: In the same plane, two lines that never intersect are called parallel lines (lines are parallel)

Property: two lines that are not parallel must intersect, and parallelism is indicated by the symbol "∥". In the same plane, there is only one straight line parallel to the straight line after passing a point outside the straight line.

2. Line-plane parallelism

Judgment theorem:

Theorem 1: If a straight line out of plane is parallel to a straight line in this plane, it is parallel to this plane.

Theorem 2: If a straight line out of the plane is perpendicular to the perpendicular of this plane, then this straight line is parallel to this plane.

property:

property 1: if a straight line is parallel to a plane, the intersection of any plane passing through the straight line and this plane is parallel to the straight line.

property: if a straight line is parallel to a plane, it is perpendicular to the plane.

3. Face-to-face parallelism

Judgment theorem:

Theorem 1: If two planes are perpendicular to the same straight line, then the two planes are parallel.

Theorem 2: If two intersecting straight lines in a plane are parallel to another plane, then the two planes are parallel.

Theorem 3: If two intersecting straight lines in one plane are parallel to two intersecting straight lines in another plane, then the two planes are parallel.

property:

property 1: two planes are parallel, and any straight line in one plane is parallel to the other plane.

property 2: two parallel planes intersect with the third plane respectively, and the intersection lines are parallel.

property 3: two planes are parallel, and a straight line perpendicular to one plane must be perpendicular to the other plane. (judging the inverse theorem of Theorem 1)

Extended data:

A simple method for judging the parallelism of lines:

Two straight lines are cut by a third straight line in the same plane. If the congruence angles are equal, then the two straight lines are parallel. It can also be simply said:

1. Two straight lines are parallel with the same angle

In the same plane, two straight lines are cut by a third straight line. If the internal dislocation angle is equal, then the two straight lines are parallel. It can also be simply said:

2. The internal dislocation angle is equal and two straight lines are parallel

In the same plane, two straight lines are cut by a third straight line. If the internal angles of the same side are complementary, then the two straight lines are parallel. It can also be simply said:

3. Two straight lines are parallel to each other.

Baidu Encyclopedia-Determination of Parallel Lines

Baidu Encyclopedia-Line-Plane Parallelism

Baidu Encyclopedia-Plane Parallelism