? (1) Two straight lines intersect into four angles, and two angles with a common vertex but no common edge are called antipodal angles;

? Two sides of one angle are opposite extension lines of two sides of another angle, which is called antipodal angle.

In fact, two straight lines intersect, in which two non-adjacent angles are diagonal angles and the adjacent angles are adjacent complementary angles.

2 the nature of the vertex angle; The vertex angles are equal.

○3 Two mutually adjacent complementary angles must be complementary, but the complementarity of the two angles is not necessarily mutually adjacent complementary angles;

○4 The antipodal angle has a common vertex and no common edge; Adjacent complementary angles have a common vertex and a common edge.

Nature of vertical line:

○ 1 There is only one straight line perpendicular to the known straight line at a point outside the straight line;

2 Of all the line segments connecting a point outside the straight line with a point on the straight line, the vertical line segment is the shortest.

Definition of the distance from a point to a straight line: the length from a point outside a straight line to the vertical section of this straight line is called the distance from a point to a straight line.

4. Parallel axiom (that is, the basic properties of parallel lines)

After passing a point outside the straight line, there is one and only one straight line parallel to this straight line. From the parallel axiom, we can also get an inference-the basic properties of parallel lines:

Theorem: If two straight lines are parallel to the third straight line, then the two straight lines are also parallel to each other.

Determination of parallel lines

1. Judgment axiom of parallel lines: two straight lines are cut by the third straight line. If congruent angles are equal, two straight lines are parallel.

To put it simply: the same angle is equal and two straight lines are parallel.

2. Judgment theorem of parallel lines: two straight lines are cut by the third straight line. If the internal dislocation angles are equal, two straight lines are parallel.

To put it simply: the internal dislocation angles are equal and the two straight lines are parallel.

3. Judgment theorem of parallel lines: two straight lines are cut by the third straight line. If the internal angles on the same side are complementary, then the two straight lines are parallel.

To put it simply: the internal angles on the same side are complementary and the two straight lines are parallel.

4. In the same plane, if two straight lines are perpendicular to the same straight line at the same time, the two straight lines are parallel.

Properties of parallel lines

Emphasis: Three property theorems of parallel lines. Difficulties: the application of property theorem.

Hot spot: apply the property theorem of parallel lines to transform angles.

1. Properties of parallel lines

Axiom (1): Two parallel lines are cut by a third line, and their congruence angles are equal. It can be simply described as: two straight lines are parallel and the same angle is equal.

(2) Theorem: Two parallel lines are cut by the third line, and the internal dislocation angles are equal. It can be simply described as: two straight lines are parallel and the internal dislocation angles are equal.

(3) Theorem: Two straight lines are cut by the third straight line and complement each other. It can be simply described as: two straight lines are parallel and complementary.

2. The properties of parallel lines are summarized as follows:

(1) Two straight lines are parallel, with the same position angle and internal dislocation angle, and the internal angles on the same side are complementary.

(2) A straight line perpendicular to one of the two parallel lines must be perpendicular to the other.

(2) The concepts of vertex angle and adjacent complementary angle.