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.
Whether to admit this axiom is the distinguishing standard between Euclidean geometry and non-Euclidean geometry; All the junior high school mathematics we study belongs to the category of European geometry.
4. Of all the line segments connecting a point outside the straight line with points on the straight line, the vertical line segment is shortest.
5. 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.
6. Two straight lines are cut by a third straight line. If congruent angles are equal, two straight lines are parallel.
7. Two parallel lines are cut by a third straight line and have the same angle.
8. Two sides and their included angles correspond to the congruence of two triangles. (Nordic Airlines).
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.
Introduction to mathematics:
Aristotle defined mathematics as "quantitative science", which lasted until18th century. /kloc-since the 0/9th century, mathematical research has become more and more rigorous, and it has begun to involve abstract topics such as group theory and projection geometry that have no clear relationship with quantity and measurement. Mathematicians and philosophers have begun to put forward various new definitions.
Some of these definitions emphasize the deductive nature of a lot of mathematics, some emphasize its abstraction, and some emphasize some themes in mathematics. Even among professionals, the definition of mathematics has not been reached. Whether mathematics is an art or a science has not even been decided. Many professional mathematicians are not interested in the definition of mathematics or think it is undefined. Some just said, "Mathematics is done by mathematicians."