(2) The internal dislocation angles are equal and the two straight lines are parallel;

(3) The internal angles on the same side are complementary and the two straight lines are parallel;

(4) In the same plane, two straight lines perpendicular to the same straight line are parallel.

Properties: (1) Two straight lines are parallel and have the same complementary angle;

(2) The two straight lines are parallel and the internal dislocation angles are equal;

(3) Two straight lines are parallel and complementary.

The judgment and nature of parallel lines are all about the graph where two lines are cut by the third line, which can be said to be the same necessary premise for them. The difference between them is that the nature of parallel lines and the conditions and conclusions in judging parallel lines are just the opposite:

The "judgment" of parallel lines is to judge whether two straight lines are parallel. First of all, we should study the quantitative relationship among congruent angle, internal angle and ipsilateral internal angle. When we know that the congruent angles are equal or the internal angles are equal or the internal angles on the same side are complementary, we can judge that two straight lines are parallel. They are judgments from "number" to "shape"

The "nature" of parallel lines is that when two lines are known to be parallel, we can deduce the quantitative relationship between the same angle, the same internal angle and the complementary internal angle of the same side, that is, the nature of graphic "parallel lines". They are reasoning from "shape" to "number".