Definition of 1. Fraction: If A and B represent two algebraic expressions and B contains letters, then the formula A/B is called a fraction.

The condition that a fraction is meaningful is that the denominator is not zero, and the condition that the value of a fraction is zero is that the numerator is zero and the denominator is not zero.

2. The basic nature of the fraction: the numerator of the fraction is multiplied by the denominator or divided by the algebraic expression that is not equal to 0, and the value of the fraction remains unchanged.

General and approximate fractions of fractions: the key is to find the least common multiple of denominator and factorization factor.

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.

The axiom of parallelism passes through a point outside a straight line, and one and only one straight line is parallel to this straight line.

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

At the same angle, two straight lines are parallel.

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

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, the theorem of the sum of the interior angles of a triangle: the sum of the three interior 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 inner angles that are not adjacent to it.

20. Inference 3: An outer angle of a triangle is greater 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 a point on the bisector of an angle to both sides of the angle is equal.

Theorem 2: The point to which both 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.

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).

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 midline of 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 equal distance at both ends of the line segment.

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

Theorem 2: If two figures are symmetrical about a straight line, then the symmetry axis is the perpendicular 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, 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 the hypotenuse C, that is

47. Inverse theorem of Pythagorean theorem: If three sides of a triangle are related, then this triangle is a right triangle.

Theorem: 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 of the sum of internal angles of polygons: the sum of internal angles of n polygons is equal to (n-2) × 180.

5 1, inference: the sum of the external angles of any polygon is equal to 360.

52. parallelogram property theorem 1: the diagonals of parallelograms are equal.

53. parallelogram property theorem 2: the opposite sides of a parallelogram are equal.

54. Inference: The parallel lines sandwiched between two parallel lines are equal.

55. parallelogram property theorem 3: diagonal bisection of parallelogram.

56. parallelogram decision theorem 1: two groups of quadrilaterals with equal diagonals are parallelograms.

57. parallelogram judgment theorem 2: two sets of quadrilaterals with equal opposite sides are parallelograms.

58. parallelogram decision theorem 3: quadrilaterals with diagonal lines bisecting each other are parallelograms.

59. parallelogram judgment 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: 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 the diamond are perpendicular to each other, and each diagonal line bisects a set of diagonal lines.

66, diamond area = half of the diagonal product, namely

67. Diamond Decision Theorem 1: A quadrilateral with four equilateral sides is a diamond.

68. Diamond Decision Theorem 2: Parallelograms with mutually perpendicular diagonals are diamonds.

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

70. Theorem 2 of Square Properties: The two diagonals of a square are equal and bisected vertically, and each diagonal bisects a set of diagonals.

7 1, Theorem 1: Two centrally symmetric graphs are congruent.

72. Theorem 2: For two graphs with symmetric centers, the straight line connecting the symmetric points passes through the symmetric center and is equally divided by the symmetric center.

73. Inverse Theorem: If a straight line connecting the corresponding points of two graphs passes through a certain point and is bounded by this point.

If the point is split in two, then the two graphs are symmetrical about the point.

74. Theorem of isosceles trapezoid properties: The two angles of isosceles trapezoid on the same base are equal.

75. The two diagonals of an isosceles trapezoid are equal.

76, isosceles trapezoid judgment theorem: a trapezoid with two equal angles on the same bottom is an isosceles trapezoid.

77. A trapezoid with equal diagonal lines is an isosceles trapezoid.

78. Theorem of Equal Segment of Parallel Lines: If a group of parallel lines are cut on a straight line,

Equal, then the line segments cut on other straight lines are also equal.

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.

80. Inference 2: A straight line passing through the midpoint of one side of a triangle and parallel to the other side will be equally divided.

Trilaterality

8 1, the midline theorem of triangle: the midline of triangle is parallel to and equal to the third side.

Half of

82. Trapezoidal mean value theorem: the midline of a trapezoid is parallel to the two bottoms, which is equal to the sum of the two bottoms.

Half l = (a+b) ÷ 2s = l× h。

83. The basic properties of the ratio (1) If a:b=c:d, then ad=bc.

If ad=bc, then a: b = c: d.

84.(2) Combinatorial properties If a/b=c/d, then (A B)/B = (C D)/D.

85.(3) Isometric Properties If a/b=c/d=…=m/n(b+d+…+n≠0), then

(a+c+…+m)/(b+d+…+n)=a/b multiplication and factorization A2-B2 = (A+B), a3+b3=(a+b)(a2-ab+b2) A3-B3 =

Trigonometric inequality | a+b |≤| a |+b|, | a-b |≤| a |+b |, | a |≤b < =>；; -b≤a≤b，

|a-b|≥|a|-|b| -|a|≤a≤|a|

Solution of one yuan and two sides

The relationship between root and coefficient Note: Vieta theorem.

discriminant

Note: The equation has two equal real roots.

Note: The equation has two unequal real roots.

Note: The equation has no real root, but has a plurality of yokes.

The sum of the first n terms of some series

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