The line segment between two points is the shortest.

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

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

One and only one straight line is perpendicular to the known straight line.

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

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

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

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

1 1 are complementary and 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.

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

16 infers that the difference between two sides of a triangle is smaller than the third side.

The sum of the internal angles of 17 triangle is equal to 180.

18 infers that the two acute angles of 1 right triangle are complementary.

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

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.

The corner axiom has two triangles with equal angles.

The axiom of angles and angles has two angles and two triangles with equal corresponding sides.

It is inferred that there are two angles, and the opposite side of one angle corresponds to the congruence of two triangles.

The 25-sided axiom has two triangles corresponding to three sides.

The axiom of hypotenuse and right-angled side has the coincidence of hypotenuse and right-angled side corresponding to two right-angled triangles.

Theorem 1 The distance between a point on the bisector of an angle and both sides of the angle is equal.

Theorem 2 is a point with equal distance on both sides of an angle, which is on the bisector of this angle.

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

Property theorem of isosceles triangle 30. The two base angles of an isosceles triangle are equal.

3 1 Inference 1 The bisector of the vertices of an isosceles triangle bisects the base and is perpendicular to the base.

The bisector of the top corner, the midline of the bottom edge and the height of the isosceles triangle coincide.

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

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

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.

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

The center line of the hypotenuse of a right triangle is equal to half of the hypotenuse.

Theorem 39 The distance between the point on the vertical line of a line segment and the two endpoints of the line segment is equal.

The inverse theorem and the point where the two endpoints of a line segment are equidistant are on the middle vertical line of this line segment.

The perpendicular bisector of the 4 1 line segment can be regarded as the set of all points with equal distance from both ends of the line segment.

Theorem 42 1 Two graphs symmetric about a line are conformal.

Theorem 2: If two figures are symmetrical about a straight line, then the symmetry axis is the perpendicular to the straight line connecting the corresponding points.

Theorem 3 Two graphs 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 bisected vertically by the same straight line, then the two graphs are symmetrical about this straight line.

46 Pythagorean Theorem The sum of squares of two right angles A and B of a right triangle is equal to the square of the hypotenuse C, that is, A+B = C.

47 Pythagorean Theorem Inverse Theorem If the lengths of three sides of a triangle A, B and C are related, and a+b=c, then this triangle is a right triangle.

The sum of the quadrilateral internal angles of Theorem 48 is equal to 360.

The sum of the external angles of the quadrilateral is equal to 360.

The theorem of the sum of internal angles of 50 polygons is that the sum of internal angles of n polygons is equal to (n-2) × 180.

5 1 It is inferred that the sum of the external angles of any polygon is equal to 360.

52 parallelogram property theorem 1 parallelogram diagonal equality

53 parallelogram property theorem 2 The opposite sides of parallelogram are equal

It is inferred that the parallel segments sandwiched between two parallel lines are equal.

55 parallelogram property theorem 3 diagonal bisection of parallelogram.

56 parallelogram decision theorem 1 Two groups of parallelograms with equal diagonals are parallelograms.

57 parallelogram decision theorem 2 Two groups of parallelograms with equal opposite sides are parallelograms.

58 parallelogram decision theorem 3 A quadrilateral whose diagonal is bisected is a parallelogram.

59 parallelogram decision theorem 4 A group of parallelograms with equal opposite sides are parallelograms.

60 Rectangle Property Theorem 1 All four corners of a rectangle are right angles.

6 1 rectangle property theorem 2 The diagonals of rectangles are equal

62 Rectangular Decision Theorem 1 A quadrilateral with three right angles is a rectangle.

63 Rectangular Decision Theorem 2 Parallelograms with equal diagonals are rectangles

64 diamond property theorem 1 all four sides of the diamond are equal.

65 Diamond Property Theorem 2 Diagonal lines of diamonds are perpendicular to each other, and each diagonal line bisects a set of diagonal lines.

66 Diamond area = half of diagonal product, that is, S=(a×b)÷2.

67 diamond decision theorem 1 A quadrilateral with four equilateral sides is a diamond.

68 Diamond Decision Theorem 2 Parallelograms whose diagonals are perpendicular to each other are diamonds.

69 Theorem of Square Properties 1 All four corners of a square are right angles and all four sides are equal.

Theorem of 70 Square Properties 2 Two diagonal lines of a square are equal and bisected vertically, and each diagonal line bisects a set of diagonal lines.

Theorem 7 1 1 is congruent with respect to two centrosymmetric graphs.

Theorem 2 About two graphs with central symmetry, the connecting lines of symmetric points both pass through the symmetric center and are equally divided by the symmetric center.

Inverse Theorem If a straight line connecting the corresponding points of two graphs passes through a point and is bisected by the point, then the two graphs are symmetrical about the point.

The property theorem of isosceles trapezoid is that two angles of isosceles trapezoid on the same base are equal.

The two diagonals of an isosceles trapezoid are equal.

76 isosceles trapezoid decision theorem A trapezoid with two equal angles on the same base is an isosceles trapezoid.

A trapezoid with equal diagonal lines is an isosceles trapezoid.

Theorem of parallel lines bisecting line segments If a group of parallel lines have the same line segment on a straight line, so do the line segments on other straight lines.

79 Inference 1 A straight line passing through the midpoint of one waist of a trapezoid and parallel to the bottom will bisect the other waist.

Inference 2 A straight line passing through the midpoint of one side of a triangle and parallel to the other side will bisect the third side.

The median line theorem of 8 1 triangle The median line of a triangle is parallel to the third side and equal to half of it.

The trapezoid midline theorem is parallel to the two bases and is equal to half the sum of the two bases.

L=(a+b)÷2 S=L×h