Summary and induction of the basic theorems of junior high school mathematics
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.
10, internal dislocation angles are equal, and 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, the sum of two sides of a theorem triangle is greater than the third side.
16, the difference between two sides of the inference triangle is smaller than the third side.
17, the sum of the internal angles of the triangle and the theorem triangle is equal to 180?
18, it is inferred 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 inner angles that are not adjacent to it.
20. Inference 3 The outer angle of a triangle is larger than any inner angle that is not adjacent to it.
2 1, the corresponding edge of congruent triangles is equal to the corresponding angle.
22. The edge axiom (SAS) has two edges, and their included angle corresponds to the congruence of two triangles.
23. The corner axiom (ASA) has two corners and two triangles with equal corresponding sides.
24. Inference (AAS) has two angles, and the opposite side of one angle corresponds to the congruence of two triangles.
25. The side-by-side axiom (SSS) has the congruence of two triangles whose three sides correspond to each other.
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 the point on the bisector of the angle to both sides of the angle is equal.
28. Theorem 2 The point where two sides of an angle are equidistant is on the bisector of this angle.
29. The bisector of an angle is the set of all points with equal distance to both sides of the angle.
30, the nature theorem of isosceles triangle The two bottom angles of an isosceles triangle are equal (that is, equilateral angles)
3 1, inference 1 The bisector of the vertex of the isosceles triangle bisects the base and is perpendicular to the base.
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. Decision theorem of isosceles triangle If a triangle has two equal angles, then the sides of the two angles are also equal (equal angles and equal sides).
35. Inference 1 A triangle with three equal angles is an equilateral triangle.
36. Inference 2 has an angle equal to 60? An isosceles triangle is an equilateral triangle.
37. In a right triangle, if an acute angle equals 30? Then the right angle it faces is equal to half of the hypotenuse.
38. The midline 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 this line segment.
40. The inverse theorem and the equidistant point between the two endpoints of a line segment are on the 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 equal distance at both ends of the line segment.
42. Theorem 1 Two graphs symmetric about a straight line are conformal.
43. Theorem 2 If two figures are symmetrical about a straight line, then the symmetry axis is the perpendicular line connecting the corresponding points.
44. 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, then the two graphs are symmetrical about this straight line.
46. Pythagorean Theorem The sum of squares of two right-angled sides A and B of a right-angled triangle is equal to the square of hypotenuse C, that is, a2+b2=c2.
47. Inverse Theorem of Pythagorean Theorem If the three sides of a triangle A, B and C are related to a2+b2=c2, then this triangle is a right triangle.
48. The sum of the internal angles of a quadrilateral is equal to 360?
49. The sum of the external angles of the quadrilateral is equal to 360?
50. Theorem The sum of the interior angles of a polygon is equal to (n-2)? 180?
5 1, inferring that the sum of any multilateral external angles is equal to 360?
52. parallelogram property theorem 1 parallelogram diagonal is equal
53, parallelogram property theorem 2 The opposite sides of a parallelogram are equal
54. 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 judgment theorem 1 Two groups of quadrilaterals with equal diagonals are parallelograms.
57. parallelogram decision theorem 2 Two groups of quadrilaterals with equal opposite sides are parallelograms.
58. parallelogram decision theorem 3 The quadrilateral whose diagonals are bisected is a parallelogram.
59. parallelogram decision theorem 4 A set of parallelograms with equal opposite sides is a parallelogram.
60. Theorem of Rectangular Properties 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 A parallelogram with equal diagonals is a rectangle.
64. Diamond Property Theorem 1 All four sides of a 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 the 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 with diagonal lines perpendicular to each other are diamonds.
69. Theorem of Square Properties 1 Four corners of a square are right angles and four sides are equal.
70. Theorem of Square Properties 2 The two diagonals of a square are equal and bisected vertically, and each diagonal bisects a set of diagonals.
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