There is only one straight line between two points.
2
The line segment between two points is the shortest.
three
The complementary angles of the same angle or the same angle are equal.
four
The complementary angles of the same angle or the same angle are equal.
five
One and only one straight line is perpendicular to the known straight line.
six
Of all the line segments connecting the outer point and the point on the line, the vertical line segment is the shortest.
seven
Parallel axiom
After passing a point outside the straight line, there is one and only one straight line parallel to this straight line.
eight
If both lines are parallel to the third line, then the two lines are also parallel to each other.
nine
The isosceles angles are equal and the two straight lines are parallel.
10
Internal dislocation angles are equal and two straight lines are parallel.
1 1
The internal 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 have equal internal angles.
14
These two lines are parallel and complementary.
15
theorem
The sum of two sides of a triangle is greater than the third side.
16
reason
The difference between two sides of a triangle is smaller than the third side.
17
Theorem of sum of interior angles of 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
The outer angle of a triangle is equal to the sum of two non-adjacent inner angles.
20
Inference 3
The 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-sided axiom (SAS)
Two triangles with two sides and their included angles equal.
23
Corner axiom (
ASA) Two triangles with two corners, and their clamping edges are equal.
24
reason
There are two angles, and the opposite side of one angle corresponds to the coincidence of two triangles.
25
Edge axiom
Two triangles with three corresponding equilateral sides are congruent.
26
Axiom of hypotenuse and right angle (HL)
Two right-angled triangles with a hypotenuse and a right-angled side are congruent.
27
Theorem 1
A point on the bisector of an angle is equal to the distance on both sides of the angle.
28
Theorem 2
A point on the bisector of an angle that is equidistant from both sides of the angle.
29
The bisector of an angle is the set of all points with equal distance to both sides of the angle.
30
Property theorem of isosceles triangle
The two base angles of an isosceles triangle are equal.
(i.e. equilateral and equiangular)
3 1
Inference 1
The bisector of the vertices of an isosceles triangle bisects 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.
33
Inference 3
All angles of an equilateral triangle are equal, and each angle is equal to 60.
34
Judgement theorem of isosceles triangle
If the two angles of a 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.
36
reason
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, the right side it faces is equal to half of the hypotenuse.
38
The center line of the hypotenuse of a right triangle is equal to half of the hypotenuse.
39
theorem
The point on the vertical line of a line segment is equal to the distance between the two endpoints of the line segment.
40
Inverse principle
On the perpendicular bisector of a line segment, a point equidistant from the two endpoints of the line segment.
4 1
The middle vertical line of a line segment can be regarded as a set of all points with the same distance at both ends of the line segment.
Forty two.
Theorem 1
The congruence of two figures symmetric about a straight line.
43
theorem
2
If two figures are symmetrical about a straight line, then the symmetry axis is the middle vertical line connecting the corresponding points.
Theorem 3
Two figures are symmetrical about a straight line. If their corresponding line segments or extension lines intersect, then the intersection point is on the axis of symmetry.
45 inverse theorem
If the straight line connecting the corresponding points of two graphs is vertically bisected by the same straight line, the two graphs are symmetrical about this straight line.