1, the straight line is parallel to the plane: definition: the straight line and the plane have nothing in common. Judgment: A straight line not in a plane is parallel to a straight line in a plane, then the straight line is parallel to this plane (derived from parallel lines). Property: The straight line is parallel to the plane. If the plane passing through this line intersects this plane, then this line is parallel to the intersection of the two planes.
2. The plane is parallel to the plane: Definition: There is nothing in common between the two planes. Judgment: Two intersecting straight lines in one plane are parallel to the other plane, so the two planes are parallel. Property: if two planes are parallel, the straight line in one plane is parallel to the other plane; If two parallel planes intersect the third plane at the same time, their intersection lines are parallel.
3. The positional relationship between two straight lines in space: intersecting straight lines (with only one common point) and parallel straight lines (with no common point on the same plane).
Two parallel lines intersect with the third straight line, which complement each other. The judgment theorem and property theorem of two parallel planes are not only logically related to the parallelism of straight lines and planes, but also closely related to the parallelism of straight lines and planes.
At a point outside the straight line, there is one and only one straight line parallel to this straight line. If a straight line is perpendicular to two intersecting lines on a plane, it is perpendicular to the plane. The included angle between the straight line and the plane: 0,90 degrees, the acute angle formed by the diagonal line in the plane and its projection in the plane, especially 90 degrees vertical, 0 degrees in the plane or parallel.
Determination method of parallel lines:
1. On the same plane, two straight lines are cut by the third straight line. If congruent angles are equal, two straight lines are parallel. It can also be simply said that the same angle is equal and two straight lines are parallel.
2. On the same plane, two straight lines are cut by the third straight line. If the offset angles are equal, the two lines are parallel. It can also be simply said that the internal dislocation angles are equal and the two straight lines are parallel.
3. On the same plane, two straight lines are cut by the third straight line. If the internal angles on the same side are complementary, the two straight lines are parallel. It can also be simply said that the internal angles on the same side are complementary and the two straight lines are parallel.