Parallel lines, parallel lines and parallel surfaces are interrelated and mutually transforming relationships. "Parallel lines", "parallel lines and planes", and "parallel planes" are cause and effect, but are mutually transformed and closely connected. "Line parallelism" is the basis of all parallel relationships. For example: "Parallel lines", "Parallel lines" and "Parallel surfaces" are like three cities in my country, connected to each other through rivers and roads. "Parallel" is the control center, regulating the transactions of the three cities. .

The definition of parallel lines: If two straight lines have no common point in the same plane, they are said to be parallel. Axiom: Two straight lines parallel to the same straight line are parallel to each other. (Transitivity of Parallel Lines in Space) Theorem: If the same angles are equal, or the interior angles are equal, or the interior angles on the same side are complementary, the two straight lines are parallel.

The definition of line-plane parallelism: a straight line and a plane have countless common points, and the straight line is said to be in the plane. Axiom: If two points on a straight line lie in a plane, then the straight line lies in this plane. Axiom: Any two points determine a straight line, and three points on an inconsistent line determine a plane; two intersecting straight lines and two parallel straight lines determine a plane.

The definition of face-to-face parallelism: two planes are said to be parallel if they have no common point. Axiom: Two planes parallel to the same plane are parallel to each other. (Transitivity of Parallel Planes in Space) Theorem: If two intersecting straight lines in a plane are parallel to another plane, then the two planes are parallel.