1, there is only one straight line between two points.

2. The line segment between two points is the shortest.

3. The complementary angles of the same angle or equal angle are equal.

4. The complementary angles of the same angle or equal angle are equal.

5. There is one and only one straight line perpendicular to the known straight line.

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

7. The parallel axiom passes through a point outside the straight line, and there is only one straight line parallel to this straight line.

8. If two straight lines are parallel to the third straight line, the two straight lines are also parallel to each other.

9. The same angle is equal, and two straight lines are parallel.

Extension:

I. Axioms

It is a basic proposition based on the self-evident basic facts of human reason, which has been tested by human repeated practice for a long time and needs no further proof. If there is no hypothesis, nothing can be deduced except tautology. Axiom is the basic assumption that leads to a specific set of deductive knowledge.

Axiom: It is the basic mathematical knowledge that people have summed up in their long-term practice, as the basis for judging the truth of other propositions.

Theorem: The true proposition obtained by reasoning is called "theorem", and this reasoning method is also called "proof"

Second, the axiomatic system (Axiomatic System)

It is to axiomatize a scientific theory and study it in an axiomatic way. Every scientific theory is a system composed of a series of concepts and propositions. The realization of axiomatization is:

1, select a group of initial concepts from its many concepts, and the rest of the concepts in this theory are introduced by definition from the initial concepts, which are called derived concepts;

2. Select a set of axioms from its series of propositions, and the other propositions are derived from axioms by using logical rules, which are called theorems. The process of deducing theorems from axioms by applying logical rules is called proof.

Every theorem has been proved. The deductive system consisting of initial concept, derived concept, axiom and theorem is called axiom system. Initial concepts and axioms are the starting points of axiomatic systems.