There is only one straight line between the two points of junior high school geometric formula daquan 1. The shortest line segment between two points is equal to the complementary angle of the same angle or equal angle. The complementary angle of the same angle or equal angle is equal to 5. Only one straight line is perpendicular to the known straight line. 6. Of all the line segments, the shortest vertical line segment connected with a point on a straight line is 7. There is only one straight line parallel to the straight line. If two straight lines are parallel to the first straight line, then three straight lines are parallel and the two straight lines are parallel to each other. 9 isosceles angles are equal. The two lines are parallel to each other. 10 internal angles are equal. The two lines are parallel to each other. 12 internal angles are equal. 13 internal angles are equal. These two lines are parallel to each other. 1. The sum of two sides of the triangle is greater than the third side 16. The difference between two sides of a triangle is less than the sum of three internal angles of the third side 17. The two acute angles of a right triangle are complementary. The outer angle of a triangle is equal to the sum of two non-adjacent inner angles, and the outer angle of a triangle of 20 is greater than any non-adjacent inner angle. The angles corresponding to 38+0 congruent triangles are equal. A triangle congruence (SAS) with two sides and their included angles. There are two triangular congruences (ASA) with two corners and their sides in the middle. There are two triangular congruences (AAS) with two angles, and the opposite sides of one angle are equal. 25 has two triangular congruences (SSS). The congruence (HL) of two right-angled triangles with a hypotenuse and a right-angled side. The distance between 27 points on the bisector of the angle is equal to both sides of the angle. The distance between 28 points on the bisector of the angle is equal to both sides of the angle. The bisector of an angle is the set of all points with equal distance to both sides of the angle. Property theorem of 30 isosceles triangle. The bisector of the vertex angle of an isosceles triangle is equal to 365,438+0. The bottom is divided in two, and the top angle of the isosceles triangle is perpendicular to the bottom 32. The heights of the center line and the bottom of the line coincide with each other. All angles of an equilateral triangle are equal, and each angle is equal to 60 34. Judgement theorem of isosceles triangle. If a triangle has two equal angles, then the opposite sides of the two angles are also equal (equilateral). A triangle with three equal angles is an equilateral triangle. 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, then the right side it faces is equal to half of the hypotenuse. The median line of the hypotenuse of a right triangle is equal to half of the hypotenuse. The distance between a point on the vertical line of a line segment and its two endpoints is equal to 40, and the distance between the two endpoints of a line segment is equal. The equal points are on the vertical line of this line segment. The median vertical line of line segment 4 1 can be regarded as a set of all points with equal distance from both ends of the line segment. The congruence of two graphs symmetric about a line. If two figures are symmetrical about a straight line, the symmetry axis is the middle vertical line connecting the corresponding points. If their corresponding line segments or extension lines intersect, the intersection point is on the axis of symmetry. 45. If the line connecting the corresponding points of two graphs is bisected vertically by the same straight line, the two graphs are symmetrical about this straight line. 46. 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, a+b=c. If three sides of a triangle have a relationship A+B = C, then this triangle is a right-angled triangle. 48. The sum of the external angles of a quadrilateral is equal to 360 degrees. Theorem of the sum of internal angles of 50 polygons The sum of internal angles of n polygons is equal to (n-2). × 180 5 1 The external angle of any polygon is equal to 360 52. The diagonal of the parallelogram is equal to 53. The opposite sides of the parallelogram are equal to 54. The parallel line sandwiched between two parallel lines is equal to 55. Diagonal lines of parallelograms are equally divided. 56. A quadrilateral with equal diagonal lines is a parallelogram. 57. A quadrilateral with equal sides is a parallelogram. 58. Diagonal lines are equal to each other. The bisected parallelogram is parallelogram 59, and a group of parallelograms with equal opposite sides is parallelogram 60. All four corners of a rectangle are right angles 6 1. Diagonal lines of rectangles are equal. A quadrilateral with three right angles is a rectangle. The parallelogram with equal diagonal lines is a rectangle 64. The four sides of a diamond are equal. 65. Diagonal lines of the diamond are perpendicular to each other, and each diagonal line bisects a set of diagonal lines 66. Diamond face. Product = half of diagonal product, that is, S=(a×b) ÷267A. A quadrilateral with four equal sides is a rhombus with 68 diagonal lines perpendicular to each other. A parallelogram with 69 square corners is a diamond with all right angles and all four sides equal. The two diagonals of 70 squares are equal, and they are equally divided vertically. Each diagonal line is divided into two by a set of diagonal lines. 7 1 congruence of two graphs symmetric about the center. A straight line connecting the symmetrical points of two graphs symmetrical about the center passes through the center of symmetry and merges. And is bisected by the center of symmetry 73. If a line connecting the corresponding points of two graphs passes through a certain point and is split in two by the point, the two graphs are symmetrical about the point 74. The two angles of an isosceles trapezoid on the same base are equal to 75. The two diagonals of an isosceles trapezoid on the same base are equal to 76. The trapezoid with equal diagonal lines is isosceles trapezoid 77. The trapezoid with equal diagonal lines is an isosceles trapezoid 78. If the line segments are equal, the line segments cut on other lines are also equal. 79. A straight line passing through the midpoint of one waist of a trapezoid and parallel to the bottom will bisect the other waist. 80. 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 of the 8 1. triangle is parallel to the third side and equal to half of it. 82. The center line of the trapezoid is parallel to the two bottom sides and equal to half of the sum of the two bottom sides. L=(a+b)。 S=L×h 83 if a:b=c:d then ad=bc if ad=bc then a:b=c:d 84 if a/b=c/d then (A B)/B = (C D)/D 85 if a/b = c/d = … = m/n.b86. Cut off one side of a triangle parallel to the other two sides (or extension lines of both sides) and the corresponding line segment is proportional to 88. If a straight line cuts two sides of a triangle (or the extension lines of two sides), the corresponding line segments obtained are proportional, so this line is parallel to the third side 89 of the triangle and one side of the triangle, and the three sides of the triangle cut by the straight line intersecting with the other two sides are proportional to the three sides of the original triangle. The triangle formed by the intersection of a straight line parallel to one side of a triangle and other two sides (or extension lines of both sides) is similar to the original triangle (ASA). A right triangle is divided into two right triangles according to the height on the hypotenuse, which is similar to the original triangle. The two sides are in direct proportion and the included angle is equal. Two triangles are similar (SAS) 94. Three sides are proportional. Two triangles are similar (SSS). If the hypotenuse and a right-angled side of a right-angled triangle are proportional to the hypotenuse and a right-angled side of another right-angled triangle, then the two right-angled triangles are similar. The ratio of the corresponding height of similar triangles to the corresponding midline and the ratio of the corresponding angular bisector are all equal to the similarity ratio. The ratio of the circumference of similar triangles is equal to the similarity ratio. The area ratio of similar triangles is equal to the square of the similarity ratio. The sine of any acute angle is equal to its complementary angle. The cosine of any acute angle is equal to the sine of the remaining angle 100. The tangent of any acute angle is equal to the cotangent of its complementary angle. The cotangent of any acute angle is equal to the tangent of its complementary angle 10 1. A circle is a set of points whose distance from a fixed point is equal to the fixed length 102. The inside of a circle can be regarded as a set of points whose center distance is less than the radius 103. The exterior of can be regarded as a point set whose center distance is greater than the radius. 104 has the same radius as a circle or an equal circle. 105 is the locus of a point whose distance from a point to a fixed point is equal to the distance of a circle whose center is a fixed length. 106 is the locus of a point whose distance is equal to the distance between two endpoints of a known line segment. The trajectory of is the bisector of this angle 108, and the trajectory from the equidistant point of two parallel lines is a straight line parallel to and equidistant from these two parallel lines 109. Three points not on the same line determine a straight line 1 10, which is perpendicular to the diameter of the chord and bisects the chord and two arcs 165438+. The diameter of a chord (not the diameter) bisecting the chord is perpendicular to the chord, the median perpendicular of the two arcs bisecting the chord passes through the center of the circle, the diameter of one arc bisecting the chord is perpendicular to the chord, and the arcs sandwiched by two parallel chords bisecting the other arc 1 12 circle are equal. The circle is a central symmetric figure 165. 438+04 In the same circle or equal circle, the arcs are equal, the chords are equal, and the distances between the chords are equal. 1 15 In the same circle or equal circle, if two central angles, two arcs, two chords or a set of two chords have the same distance, then their corresponding quantities are the same. The circumferential angles of an arc are equal. The arc opposite to the equal circle angle in the same circle or equal circle is also equal, and the circle angle opposite to the semicircle (or diameter) is a right angle; The chord subtended by the 90 circumferential angle is 1 19. If the median line of one side of a triangle is equal to half of this side, then this triangle is a right triangle of 120. Diagonal lines of the inscribed quadrilateral are complementary, and any external angle is equal to its internal angle 12 1 ①. The straight lines L and O intersect D < R2, and the straight lines L and O are separated by d > r 122. The straight line perpendicular to this radius is the tangent of the circle. The tangent of the circle is perpendicular to the radius passing through the tangent point 124, and passes through the center of the circle. The straight line perpendicular to the tangent line must pass through the tangent point 125, and the straight line perpendicular to the tangent line must pass through the center of the circle 126. The tangent length of these lines is equal to the center of the circle, and the connecting line of this point bisects the included angle of the two tangents. The sum of two opposite sides of the circumscribed quadrangle of 127 circle is equal. The chord angle of 128 is equal to the circumferential angle of the arc pair it clamps. If the arc sandwiched by two chord angles is equal, then the two chord angles are also equal. 130 The product of two line segments divided by the intersection point in the circle. Equal to 13 1 If the chord intersects the diameter vertically, then half of the chord is the ratio of the two line segments formed by dividing it by the diameter. The term 132 is the ratio of the tangent and the secant length from a point outside the circle to the intersection of the secant and the circle. The term 133 is equal to the product of two line segments from the point outside the circle to the intersection of each secant and the circle. 438+034 If two circles are tangent, then the tangent point must be on the connecting line. 135 ① Two circles are circumscribed by D > R+R ② Two circles are circumscribed by d=R+r ③ Two circles intersect R-R < D < R+R (R > R) ④ Two circles are inscribed by D = R-R (R > R) ⑤ Two circles contain D < R. Chords/kloc- (1) The polygon obtained by connecting the points in turn is an inscribed regular N-polygon of this circle; (2) A polygon whose vertices are the intersections of adjacent tangents passing through these points is a circumscribed regular N polygon of this circle; 138 Any regular polygon has a circumscribed circle and an inscribed circle; These two circles are concentric circles; Each inner angle of a regular N-polygon is equal to (n-2) × 180. The radius of N 140 regular N polygon and point A divide the regular N polygon into 2n congruent right-angled triangles 14 1 2 p indicates the perimeter of the regular N polygon 142 the area of the regular triangle √3a/ 4 a indicates the side length is144 a. If there are K positive N corners around a vertex, since the sum of these angles should be 360, K× (n-2) 180/n = 360 is converted into the formula for calculating the arc length of (n-2)(k-2)=4 144. 180 145 sector area formula: s sector =n∏R/360=LR/2 146 inner common tangent length = d-(R-r) outer common tangent length = d-(r+r)/kloc-0.

Formula classification formula expression

Multiplication and factorization A2-B2 = (a+b) (a-b) A3+B3 = (a+b) (A2-AB+B2) A3-B3 = (A-B (A2+AB+B2))

Trigonometric inequality | A+B |≤| A |+B||||| A-B|≤| A |+B |||| A |≤ B-B≤ A≤ B.

|a-b|≥|a|-|b| -|a|≤a≤|a|

The solution of the unary quadratic equation -b+√(b2-4ac)/2a -b-√(b2-4ac)/2a

The relationship between root and coefficient x1+x2 =-b/ax1* x2 = c/a Note: Vieta theorem.

discriminant

B2-4ac=0 Note: This equation has two equal real roots.

B2-4ac >0 Note: The equation has two unequal real roots.

b2-4ac0

Parabolic standard equation y2=2px y2=-2px x2=2py x2=-2py

Lateral area of a straight prism S=c*h lateral area of an oblique prism s = c' * h.

Lateral area of a regular pyramid S= 1/2c*h' lateral area of a regular prism S= 1/2(c+c')h'

The lateral area of the frustum of a cone S = 1/2(c+c')l = pi(R+R)l The surface area of the ball S=4pi*r2.

Lateral area of cylinder S=c*h=2pi*h lateral area of cone s =1/2 * c * l = pi * r * l.

The arc length formula l=a*r a is the radian number r > of the central angle; 0 sector area formula s= 1/2*l*r

Conical volume formula V= 1/3*S*H Conical volume formula V= 1/3*pi*r2h

Oblique prism volume V=S'L Note: where s' is the straight cross-sectional area and l is the side length.

Cylinder volume formula V=s*h cylinder V=pi*r2h