1, axiom of line segment: between two points, the line segment is the shortest.

2. axiom of straight line: there is only one straight line after two o'clock.

3. Parallelism axiom: At a point outside the straight line, there is one and only one straight line parallel to the known straight line.

4. verticality: after passing through a point on the outside or straight line, there is one and only one straight line perpendicular to the known straight line.

5. Two straight lines are cut by the third straight line. If congruent angles are equal, two straight lines are parallel.

6. Two parallel lines are cut by a third straight line and have the same angle.

7. Two sides and their included angles correspond to the congruence of two triangles. (SAS)

8. Two corners and their clamping edges correspond to the coincidence of two triangles. (ASA)

9. Three sides correspond to the coincidence of two equal triangles. (SSS)

10, the corresponding edges of congruent triangles are equal, and the corresponding angles are equal.

Extended data

A method to prove that two straight lines are parallel and equal in angle;

The nature of parallel lines: two straight lines are parallel and the same angle is equal.

Two straight lines are parallel and have equal internal angles. The judgment of parallel lines with two parallel lines and complementary internal angles on the same side: the same angle is equal and the two straight lines are parallel.

Internal dislocation angles are equal and two straight lines are parallel. The internal angles on the same side are complementary and the two straight lines are parallel.

Two straight lines A and B are cut by a third straight line C (or the intersection of C of A and B). On the same side of the cutting line C, cut the corners on the same side of the two straight lines A and B.. We call these two angles congruent angles.

When two straight lines A and B are cut by a third straight line C, a "three-line octagon" will appear, which has 4 pairs of congruent angles, 2 pairs of internal angles and 2 pairs of internal angles on the same side.