Junior high school math formula summary (all) I hope it will help you with your study! 1 There is only one straight line between two points. The shortest line segment between two points is 3. The same angle or the complementary angle of the same angle is equal. 4. The same angle or the complementary angle of the same angle is equal. 5. Only one straight line is perpendicular to the known straight line. 6. Among all the line segments connected with points on a straight line, the shortest parallel axiom of a vertical line segment passes through a point outside the straight line. There is only one straight line parallel to this straight line. If both lines are parallel to the third line, the two lines are parallel to each other. The isosceles angles are equal and the two straight lines are parallel to each other. 10, the offset angles are equal, and the two straight lines are parallel to each other. 1 1 is complementary to the inner corner of the side, and the two straight lines are parallel to each other. 13, two straight lines are parallel. The internal dislocation angle is equal to 14, and the two straight lines are parallel. Theorem The sum of two sides of a triangle is greater than the third side 15. The difference between two sides of the reasoning triangle is less than the third side 17. Theorem The sum of three internal angles of a triangle is equal to 180 18. The two acute angles of a right triangle complement each other 19. Inference 2 3. The outer angle of an angle is equal to the sum of two non-adjacent inner angles. 20 Inference 3 Any corresponding side of a triangle whose outer angle is greater than its non-adjacent inner angle, 2 1 congruent triangles, and the corresponding angles are equal. 22-Angle Axiom (SAS) has a triangle congruent 23-Angle Axiom (ASA) with two sides and their included angles equal. Two angles of two triangles correspond to their sides congruent 24 Inference (AAS) Two angles of two triangles correspond to one opposite side congruent 25-sided axiom (SSS) Two triangles correspond to congruent 26 hypotenuse and right-angled axiom (HL). Two right-angled triangles with a hypotenuse and a right-angled side are congruent. Theorem 1 A point on the bisector of an angle is equal to the distance between two sides of the angle. Theorem 2 To a point with equal distance on both sides of an angle, on the bisector of this angle, the bisector of 29 angles is the set of all points with equal distance on both sides of this angle. The nature theorem of isosceles triangle 30 The two base angles of an isosceles triangle are equal (that is, equilateral and equilateral). 3 1 Inference 1 The bisector of the top angle of the isosceles triangle bisects the bottom and is perpendicular to the bisector of the top angle of the isosceles triangle with the bottom 32. The midline on the bottom edge coincides with the height on the bottom edge. Inference 3 All angles of an equilateral triangle are equal, and each angle is equal to 60 34 isosceles triangle. If a triangle has two equal angles, then the opposite sides of the two angles are also equal (equilateral) 35 Inference 1 A triangle with three equal angles is an equilateral triangle 36 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-angled 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. Theorem 39 A point on the vertical line of a line segment is equal to the distance between the two endpoints of this line segment. The inverse theorem and the point where the two endpoints of a line segment are equal. On the midline of this line segment, the midline of line segment 4 1 can be regarded as a set of all points with equal distance from both ends of the line segment. Theorem 42: Two graphs that are symmetrical about a straight line are congruent. Theorem 43: Two figures are symmetrical about a straight line, then the symmetry axis is the median vertical line 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 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-angled sides A and B of a right-angled triangle is equal to the square of the hypotenuse C, that is, the inverse theorem of A 2+B 2 = C 2. 47 Pythagorean Theorem If three sides of a triangle have a relationship A 2+B 2 = C 2, then this triangle is a right-angled triangle, and the sum of the internal angles of the quadrilateral of Theorem 48 is equal to 360 49, and the sum of the internal angles of the polygon and Theorem N is equal to (n-2). It is inferred that the sum of the external angles of any polygon is equal to 360 52, and the parallelogram property theorem 1 is flat. The line is equal to the diagonal of the parallelogram. 53 Parallelogram property theorem 2 Parallelogram opposite sides are equal. 54 Inference that parallel lines between two parallel lines are equal. 55 Parallelogram property theorem 3 Parallelogram diagonal bisection 56 Parallelogram decision theorem 1 Two groups of parallelograms with equal diagonal lines are parallelograms. 57 Parallelogram decision theorem 2 Two groups of opposite sides. The quadrilaterals equal to each other are parallelograms 58. Parallelogram decision theorem 3. The quadrilateral whose diagonal is bisected is a parallelogram 59. Parallelogram decision theorem 4. A set of parallelograms whose opposite sides are parallel to each other is a parallelogram 60. Rectangular property theorem 1. All four corners of a rectangle are right angles 6 1. Theorem of rectangle properties II. The diagonal lines of the rectangle are equal to 62. Rectangular decision making. Lie 1 A quadrilateral with three right angles is a rectangle 63. Rectangular Decision Theorem 2 A parallelogram with equal diagonal lines is a rectangle 64. Diamond Property Theorem 1 Diamond Property Theorem 65. The 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 diagonal product. That is, S= (a×b) ÷2 67 rhombus decision theorem 1 A quadrilateral with four equal sides is a rhombus 68 rhombus decision theorem 2 A parallelogram with perpendicular diagonal lines is a rhombus 69 square property theorem 1 All four corners of a square are right angles and all four sides are equal 70 square property theorem 2 Two diagonal lines of a square are equal. And bisect each other vertically, and each diagonal bisects a set of diagonal 7 1 theorem 1. On the congruence of two graphs with central symmetry. Theorem 2. For two graphs with central symmetry, the straight line connecting the symmetrical points passes through the symmetrical center and is split in two by the symmetrical center. Inverse Theorem If a straight line connecting the corresponding points of two graphs passes through a certain point and is split in two by that point, then the two graphs are symmetrical about that point. Property theorem of isosceles trapezoid. The two angles of an isosceles trapezoid on the same base are equal. The two diagonals of an isosceles trapezoid are equal. 76 isosceles trapeziums have equal angles on the same base, which is an isosceles trapezoid. The diagonal trapezoid is an isosceles trapezoid. Theorem of bisecting line segments by 78 parallel lines. If a set of parallel lines cut on a straight line are equal, then the line segments cut on other straight lines are also equal. 79 Inference 1 Through a straight line parallel to the bottom of the trapezoid, the other waist 80 must be equally divided. Inference 2 Inference 2 Through a straight line parallel to the other side of the triangle, the third side must be bisected. 8 1 The midline theorem of the triangle is parallel to the third side. And equal to half of it. The trapezium midline theorem is parallel to the two bottoms and is equal to half the sum of the two bottoms. The basic properties of L= (a+b) ÷2 S=L×h 83 (1) if a:b=c:d, then ad=bc, then a:b=c:d 84 (2) if a/b = c/d, Then (a b)/b = (c d)/d 85 (3) If A B = C/D = … = M/N (B+D++), then (A+C+...+M)/(B+D+...+N) = A/B 86 parallel segment. The corresponding line segment obtained is proportional to Theorem 88. If the corresponding line segments obtained by cutting two sides of a triangle (or extension lines of two sides) are proportional, then this line is parallel to the third side 89 of the triangle, parallel to one side of the triangle, and intersects with the other two sides. The three sides of the cutting triangle correspond to the three sides of the original triangle in proportion. Theorem 90 A straight line parallel to one side of a triangle intersects the other two sides (or extension lines of both sides), and the triangle formed is similar to the original triangle. Theorem 1 similar triangle judgment theorem 1 two angles are equal. Similarity between two triangles (ASA) 92 A right triangle divided by the height on the hypotenuse is divided into two right triangles. Similarity with the original triangle 93 Judgment Theorem 2. Two sides are proportional and the included angles are equal. Similarity between two triangles (SAS) 94 Judgment Theorem 3. Three sides are proportional. Two triangles are similar (SSS) Theorem 95 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. Theorem 96: 1 similar triangles corresponds to a high proportion. The ratio of the corresponding median line to the bisector of the corresponding angle is equal to the similarity ratio of 97. Property theorem 2. The ratio of similar triangles perimeter is equal to similarity ratio 98. Property theorem 3. The ratio of similar triangles area is equal to the square of similarity ratio 99. The sine value of any acute angle is equal to the cosine value of other angles, and the cosine value of any acute angle is equal to the sine value of other angles 100. The tangent of any acute angle is equal to the cotangent of the other angles. The cotangent value of any acute angle is equal to the tangent value of other angles 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 outer side of the circle can be regarded as a set of points whose center distance is greater than the radius of 65438. The distance from +005 to the fixed point is equal to the trajectory of the fixed-length point, which is a circle with the fixed point as the center and the radius of 106, and the trajectory of the point with the same distance from the middle vertical line of the line segment 107 to both sides of the known angle. The locus of the bisector of this angle 108 to a point with equal distance 1 10 vertical diameter theorem bisects the chord perpendicular to its diameter and bisects the two arcs opposite to the chord11inference 1 ① bisects the diameter of the chord (not the diameter) And bisect the two arcs opposite to the chord ③ bisect the diameter of one arc opposite to the chord, bisect the chord vertically and bisect the other arc opposite to the chord 1 12. It can be inferred that the arcs sandwiched by two parallel chords of circle 2 are equal. A circle 1 13 is a centrosymmetric figure whose center is on the same or equal circle 1 14 theorem. Equal central angles have equal arcs, equal chords and equal chord-to-chord distances. 1 15 It is inferred that in the same circle or equal circle, if one set of quantities in two central angles, two arcs, two chords or the distance between two chords is equal, the corresponding other set of quantities is also equal. 1 16 Theorem The circle corresponding to the arc. In the same circle or equal circle, the arc opposite to the equal circle angle is also equal. 1 18 infers that 2 semicircles (or diameters) are right angles; The chord subtended by the circumferential angle of 90 is 1 19 Inference 3 If the median line of 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 120 theorem circle. And any outer angle is equal to its inner diagonal 12 1 ①. The intersection of straight line L and ⊙ O is D R 122. 123 property theorem of tangent 124 inference that the tangent of a circle is perpendicular to the radius of the tangent point 1 25 inference that a straight line passing through the center of the circle and perpendicular to the tangent line must cross the tangent point 126 tangent length theorem draws two tangents from a point outside the circle, and their tangents. The sum of two opposite sides of the circumscribed quadrangle of a circle is equal. The tangent angle theorem is equal to the circumferential angle of the arc pair it clamps. It is deduced that if the arcs sandwiched by two chord tangent angles are equal, then the two chord tangent angles are equal to the two intersecting chords in the chord theorem circle. The product of the length of two lines divided by the intersection is equal to 13 1. It is deduced that if the chord intersects the diameter vertically, then half of the chord is the tangent and secant of the circle, which is drawn by the middle term 132 according to the ratio of two line segments formed by a point outside the circle. The tangent length is the ratio of the lengths of two lines from this point to the intersection of the secant and the circle. 133 This item infers that two secant lines are drawn from a point outside the circle, and the product of the lengths of the two lines from this point to the intersection of each secant line and the circle is equal to 134. If two circles are tangent, then the tangent point must be on the line 135 ① two circles are tangent to D > R+R ② two circles are tangent to d=R+r ③ two circles intersect R-R < D+R (R > R) ④ two circles are inscribed with D = R-R (R > R) ⑤ two circles contain D < R. Theorem 136 The intersection of two circles bisects the common chord of two circles vertically. Theorem 137 divides the circle into n (n ≥ 3): (1) The polygon obtained by connecting the points in turn is a regular n polygon inscribed in the circle; (2) The tangent of a circle passing through a point, and the polygon whose vertex is the intersection of adjacent tangents is the circumscribed regular N polygon of this circle. Theorem 138 Any regular polygon has a circumscribed circle and an inscribed circle. These two circles are concentric circles 139. Every inner angle of a regular N-polygon is equal to the radius and area of the regular N-polygon in theorem (n-2) × 180/N 140, where apome divides the regular N-polygon into 2n congruent right-angled triangles 14 1. The perimeter of a regular N polygon is 142, and the area of a regular triangle is √ 3a/4a, that is, the side length is 143. If there are K positive N-sided angles around a vertex, since the sum of these angles should be 360, k × (n-2) 180/n = 360 is converted into (n-2) (k-2)=4 144. Arc length calculation formula: L=n R/ 180 145. Sector area formula: S.