2. The shortest line segment between two points.

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. Parallelism axiom: After passing a point outside a straight line, there is one and 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.

10. The internal dislocation angles are equal and the two straight lines are parallel.

1 1. The inner angles on the same side are complementary and the two straight lines are parallel.

12. Two straight lines are parallel and have the same angle.

13. Two straight lines are parallel and the internal dislocation angles are equal.

14. Two straight lines are parallel and complementary.

15. Theorem: The sum of two sides of a triangle is greater than the third side.

16. Inference: The difference between two sides of a triangle is smaller than the third side.

17. Theorem of the sum of the internal angles of a triangle: the sum of the three internal angles of a triangle is equal to 180.

18. Inference 1: The two acute angles of a right triangle are complementary.

19. Inference 2: One outer angle of a triangle is equal to the sum of two non-adjacent inner angles.

20. Inference 3: An outer angle of a triangle is greater than any inner angle that is not adjacent to it.

2 1. congruent triangles has equal sides and angles.

22. Edge Axiom (SAS): Two triangles with equal angles between two sides.

23. Axiom of Angle (ASA): Two triangles have two angles and their sides are congruent.

24. Inference (AAS): There are two angles, and the opposite side of one angle corresponds to the congruence of two triangles.

25. Edge axiom (SSS): Two triangles with three corresponding equilateral sides are congruent.

26. Axiom of hypotenuse and right-angled side (HL): Two right-angled triangles with hypotenuse and a right-angled side are congruent.

27. Theorem 1: The distance from a point on the bisector of an angle to both sides of the angle is equal.

28. Theorem 2: Points with equal distances to both sides of an angle are on the bisector of this angle.

29. The bisector of an angle is a collection of all points with equal distance to both sides of the angle.

30. The property theorem of isosceles triangle: the two base angles of isosceles triangle are equal (that is, equilateral and equilateral).

3 1. Inference 1: The bisector of the top angle of the isosceles triangle bisects the bottom and is perpendicular to the bottom.

32. The bisector of the top angle, the median line on the bottom edge and the height on the bottom edge of the isosceles triangle coincide with each other.

Inference 3: All angles of an equilateral triangle are equal, and each angle is equal to 60.

34. Judgment theorem of isosceles triangle: If the two angles of the triangle are equal, then the opposite sides of the two angles are also equal (equilateral).

35. Inference 1: A triangle with three equal angles is an equilateral triangle.

Inference 2: An isosceles triangle with an angle equal to 60 is an equilateral triangle.

37. In a right triangle, if an acute angle is equal to 30, then the right side it faces is equal to half of the hypotenuse.

38. The median line on the hypotenuse of a right triangle is equal to half of the hypotenuse.

Theorem: The distance between the point on the vertical line of a line segment and the two endpoints of this line segment is equal.

40. Inverse Theorem: The point where the two endpoints of a line segment are equidistant is on the middle vertical line of this line segment.

4 1. The middle vertical line of a line segment can be regarded as the set of all points with the same distance at both ends of the line segment.