All mathematical formulas

1. perimeter of rectangle = (length+width) ×2 C=(a+b)×2

2. perimeter of square = side length× 4c = 4a

3. area of rectangle = length× width S=ab

4. area of square = side length× side length s. Area of parallelogram = bottom× height S=ah

7, area of trapezoid = (upper bottom+lower bottom )× height ÷ 2s = (a+b) h ÷ 2

8, diameter = radius× 2d = 2r radius = diameter ÷ 2r = d ÷. Area of circle = pi × radius × radius

Common junior high school mathematical formula

1 There is only one straight line passing through two points

2 The shortest line segment between two points

3 The complementary angle of the same angle or the same angle is equal

4 The complementary angle of the same angle or the same angle is equal

5 There is only one straight line passing through and the known straight line is vertical

6 A point outside the straight line is perpendicular to the straight line. The shortest parallel axiom of vertical line segment

7 passes through a point outside the straight line, and there is only one straight line parallel to this straight line

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

9. The congruence angle is equal, the two straight lines are parallel

1. The internal dislocation angle is equal, the two straight lines are parallel

11. The internal angles are complementary, and the two straight lines are parallel

12. Equal congruence angle

13 Two straight lines are parallel, and the internal dislocation angle is equal

14 Two straight lines are parallel. Complementarity of inner angles on the same side

15 The sum of two sides of the theorem triangle is greater than the third side

16 The difference between the two sides of the inference triangle is less than the third side

17 The sum of the inner angles of the triangle and the three inner angles of the theorem triangle is equal to 18°

18 The two acute angles of a right triangle are complementary

19 The conclusion that one outer angle of the triangle is equal to the sum of two inner angles that are not adjacent to it

2. An external angle of

21 is larger than any internal angle that is not adjacent to it. The corresponding angle of congruent triangles is equal

22. The corner axiom (SAS) has two sides and their included angles are equal.

23. The corner axiom (ASA) has two angles and their sandwiched sides are equal.

24. Inference (AAS). Two triangles with two corners and opposite sides of one corner corresponding to each other are congruent

25-side axiom (SSS) and three triangles corresponding to each other are congruent

26-hypotenuse axiom and right-angle axiom (HL). Two right-angled triangles with hypotenuse and a right-angled side are congruent

27 Theorem 1 The distance between the point on the bisector of an angle and the two sides of this angle is equal

28 Theorem 2 to the point with the same distance between the two sides of an angle, On the bisector of this angle, the bisector of angle

29 is the set of all points with equal distances to both sides of the angle

3 The property theorem of isosceles triangle. The two bottom angles of isosceles triangle are equal (that is, equilateral equilateral angles)

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

32 The bisector of the top angle of isosceles triangle, The midline on the base and the height on the base coincide with each other

33 Inference 3 All angles of an equilateral triangle are equal and each angle is equal to 6°

34 Judgment Theorem of an isosceles triangle If a triangle has two angles equal, Then the opposite sides of these 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 An isosceles triangle with an angle equal to 6 is an equilateral triangle

37 In a right triangle, If an acute angle is equal to 3, the right-angled side it subtends is equal to half of the hypotenuse

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

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

4. Inverse theorem and a point where the two endpoints of a line segment are equal. On the perpendicular bisector of this line segment

41, the perpendicular bisector of the line segment can be regarded as the set of all points with the same distance from both ends of the line segment

42 Theorem 1. Two figures symmetrical about a line are conformal

43 Theorem 2. If two figures are symmetrical about a line, then the symmetry axis is perpendicular bisector

44 Theorem 3. Two figures are symmetrical about a 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 line connecting the corresponding points of two graphs is vertically bisected by the same line, then the two graphs are symmetrical about this line

46 Pythagorean Theorem The sum of squares of two right-angled sides A and B of a right triangle is equal to the square of the hypotenuse c, That is, the inverse theorem of Pythagorean Theorem A 2+B 2 = C 2 < P > 47 If the three sides of a triangle have a relationship A 2+B 2 = C 2, Then this triangle is a right triangle

48. The sum of the inner angles of quadrilateral equals to 36°

49. The sum of the inner angles of polygon equals to 36°

5. The sum of the inner angles of theorem N-polygon equals to (n-2) × 18

51. Inferring the sum of the outer angles of any polygon equals to 36°

52. Parallelogram property theorem 1. Theorem 2: The opposite sides of a parallelogram are equal

54: Inference that parallel line segments sandwiched between two parallel lines are equal

55: Theorem 3: Diagonal lines of a parallelogram are equally divided

56: Judgment Theorem 1: Two groups of parallelograms with equal diagonal are parallelograms

57: Judgment Theorem 2: Two groups of parallelograms with equal opposite sides are parallelograms

58: Judgment of parallelograms. Theorem 3: Quadrilaterals whose diagonals are bisected each other are parallelograms

59. Quadrilaterals whose opposite sides are parallel are parallelograms

6. Rectangular property theorem 1. All four corners of a rectangle are right angles

61. Rectangular property theorem 2. Rectangular diagonal equality

62. Rectangular determination theorem 1. Quadrilaterals with three right angles are rectangles

63. Rectangular determination theorem 2. Diagonal equality. The parallelogram is a rectangle

64. The four sides of the diamond are equal

65. The diagonal lines of the diamond are perpendicular to each other, and each diagonal line bisects a set of diagonal lines

66. The diamond area = half of the diagonal product. That is, S=(a×b)÷2

67 Diamond Decision Theorem 1 A quadrilateral with four equal sides is a diamond

68 Diamond Decision Theorem 2 A parallelogram with diagonal lines perpendicular to each other is a diamond

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

7 Square Property Theorem 2 Two diagonal lines of a square are equal and equally divided. Each diagonal bisects a set of diagonal lines

71 Theorem 1: Two figures symmetrical about the center are congruent

72 Theorem 2: Two figures symmetrical about the center, the connecting lines of symmetrical points pass through the symmetrical center and are bisected by the symmetrical center

73 Inverse Theorem If the connecting lines of corresponding points of two figures pass through a certain point and are bisected by this point, Then these two figures are symmetrical about this point

74 isosceles trapezoid property theorem. The two corners of isosceles trapezoid on the same base are equal.

75 isosceles trapezoid with two diagonal lines are equal.

76 isosceles trapezoid judgment theorem. A trapezoid with two equal corners on the same base is an isosceles trapezoid.

A trapezoid with p>77 diagonal lines is an isosceles trapezoid. , then the line segments cut on other straight lines are also equal

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

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

81 The median line of a triangle is parallel to the third side. And equal to half of it

82 The median line theorem of trapezoid is parallel to the two bottoms, and equal to half of the sum of the two bottoms. L=(a+b)÷2 S=L×h

83 (1) Basic properties of proportion If a:b=c:d, then ad=bc If ad=bc, then A: b = Then (a b)/b = (c d)/d

85 (3) Isometric property If a/b = c/d = … = m/n (b+d+…+n ≠ ), then (a+c+…+m)/. The obtained corresponding line segments are proportional

87. It is inferred that a straight line parallel to one side of a triangle cuts the other two sides (or extension lines of both sides), and the obtained corresponding line segments are proportional

88 Theorem If the corresponding line segments obtained by cutting two sides (or extension lines of both sides) of a triangle by a straight line are proportional, then the straight line is parallel to the third side of the triangle

89, parallel to one side of the triangle, and intersects with the other two sides. The three sides of the cut triangle are proportional to the three sides of the original triangle.

9 Theorem A straight line parallel to one side of the triangle intersects with the other two sides (or extension lines of the two sides), and the triangle formed is similar to the original triangle.

91 Similar Triangle Decision Theorem 1 Two angles are equal. Similarity of two triangles (ASA)

92 The two right triangles divided by the height on the hypotenuse are similar to the original triangle

93 Decision Theorem 2, two sides are proportional and the included angles are equal, and two triangles are similar (SAS)

94 Decision Theorem 3, three sides are proportional. Two triangles are similar (SSS)

95 Theorem If the hypotenuse and one right-angled side of one right-angled triangle are proportional to the hypotenuse and one right-angled side of another right-angled triangle, then the two right-angled triangles are similar

96 Property Theorem 1 similar triangles corresponds to a high ratio, The ratio of the corresponding midline to the bisector of the corresponding angle is equal to the similarity ratio

97 Property Theorem 2 The ratio of similar triangles perimeter is equal to the similarity ratio

98 Property Theorem 3 The ratio of similar triangles area is equal to the square of the similarity ratio

99 The sine value of any acute angle is equal to the cosine value of its complementary angle, and the cosine value of any acute angle is equal to the sine value of its complementary angle

1 The tangent value of any acute angle is equal to its complementary angle. The cotangent value of any acute angle is equal to the tangent value of its complementary angle

11 A circle is a set of points whose distance from a fixed point is equal to a fixed length

12 The inside of a circle can be regarded as a set of points whose distance from the center is less than the radius

13 The outside of a circle can be regarded as a set of points whose distance from the center is greater than the radius

14 The radius of the same circle or an equal circle is equal to

15 The trajectory of points whose distance from a fixed point is equal to the fixed length. The locus of the point where the distance between the circle

16 with a fixed length and the two endpoints of the known line segment is equal is the locus of the point where the distance between the perpendicular bisector

17 of the line segment and the two sides of the known angle is equal, the locus of the bisector

18 of this angle to the point where the distance between the two parallel lines is equal, and the three points of the theorem

19 which are parallel to these two parallel lines and are not on the same line determine one.

11 Vertical Diameter Theorem bisects the chord perpendicular to the diameter of the chord and bisects the two arcs opposite to the chord

111 Inference 1 ① bisects the diameter of the chord (not the diameter) perpendicular to the chord, and bisects the two arcs opposite to the chord

② perpendicular bisector of the chord passes through the center of the circle, and bisects the two arcs opposite to the chord

③ bisects the diameter of an arc opposite to the chord and bisects the chord vertically. And the other arc bisecting the chords

112 infers that the arcs sandwiched by two parallel chords of 2 circles are equal

113 A circle is a central symmetrical figure with the center of the circle as the symmetrical center

114 Theorem In the same circle or an equal circle, the arcs subtended by equal central angles are equal, the chords subtended are equal, and the chord center distances of the chords subtended are equal

115 infers that they are in the same circle or an equal circle. If one of the two central angles, two arcs, two chords or the chord-to-chord distance of two chords is equal, then the other groups of quantities corresponding to them are equal < P > Theorem p>116 The circumferential angle of an arc is equal to half of the central angle it faces

117 Inference 1 The circumferential angles of the same arc or the same arc are equal; In the same circle or equal circle, the arcs subtended by equal circumferential angles are also equal

118 It is inferred that the circumferential angles subtended by two semicircles (or diameters) are right angles; The chord subtended by the circumferential angle of 9 is the diameter

119 Inference 3 If the median line on one side of a triangle is equal to half of this side, then this triangle is the diagonal complement of the inscribed quadrilateral of the right triangle

12 theorem circle. And any external angle is equal to its internal diagonal

121① line L and ⊙O intersect D < r

② line L and ⊙O are tangent d=r

③ line L and ⊙O are separated D > r

122. The judgment theorem of tangent passes through the outer end of the radius and the line perpendicular to this radius is the tangent of the circle < A straight line with the center of the circle and perpendicular to the tangent must pass through the tangent point

125 Inference 2 A straight line passing through the tangent point and perpendicular to the tangent must pass through the center of the circle

126 The tangent length theorem leads to two tangents of a circle from a point outside the circle, and their tangents are equal in length. The connecting line between the center of the circle and this point bisects the included angle of the two tangents

127 The sum of the two opposite sides of the circumscribed quadrilateral of a circle is equal

128 The chord tangent angle is equal to the circumferential angle of the arc pair it clamps

129 It is inferred that if the arcs clamped by the two chord tangent angles are equal, then the two chord tangent angles are equal

13 The two intersecting chords in the circle intersect the chord theorem. The product of the length of the two lines divided by the intersection point is equal

131 Inference that if the chord intersects the diameter vertically, then half of the chord is the median of the proportion of the two line segments formed by its diameter

132 The tangent line theorem leads to the tangent and secant of the circle from a point outside the circle, and the tangent line length is the median of the length of the two lines from this point to the intersection point of the secant and the circle

133 Inference of the two secant lines leading to the circle from a point outside the circle. The product of the length of the two lines from this point to the intersection of each secant and the circle is equal

134 If the two circles are tangent, then the tangent point must be on the connecting line

135① The two circles are circumscribed by D > R+R ② The two circles are circumscribed by D = R.