What is the name of children's photography at the entrance of Faxiang Lane, Jinger Road, Jinan?

Summary of junior high school mathematics knowledge points

The formula of number and algebra A: 1, and reasonable positive and negative decimals: ① integer → integer//negative integer ② fraction →/negative.

Number axis of basic knowledge points: ① Draw the horizontal line of a straight line, select a designated straight line with the length as the unit along the line point representing 0 (origin), and the correct direction is positive to get the number axis. ② Any rational number can be expressed as a point in several lines. (3) If the signs of two numbers are different, then what we call the inverse of a number is also called two numbers. The number of axes represented on the plane, two points opposite to each other, and the origin of both sides are equal distances and origins. (4) At two o'clock, the number of logarithmic axes on the right is greater than that on the left. Positive numbers greater than 0, negative numbers, positive numbers less than 0 and greater than negative numbers.

Absolute value: ① The number of axes is the absolute value of the number corresponding to the point called the distance from the origin. (2) The absolute value itself is a positive number, the absolute value of a negative number is its inverse number, and the absolute value of 0 is 0. The relative size of two negative numbers, not the absolute value.

Operation of rational numbers: addition: ① Sum of consecutive numbers, taking the same sign and the sum of absolute values. ② When different symptoms are added together, the absolute values are equal, all of which are 0; The absolute value of inequality, take the number of symbols with larger absolute value and subtract it from the smaller absolute value with larger absolute value. ③ Add a number 0 and keep it unchanged.

Subtraction: Subtract the reciprocal of a number and add it.

Multiplication: ① these two numbers are multiplied, and the sign of the same number is opposite, and the absolute value is multiplied. ② Multiply any number by 0. ③ The reciprocal of the product of two rational numbers.

Teacher: ① Dividing by a number equals multiplying by the reciprocal of a number. ②0 cannot be a divisor.

Power: A graph with n identical factors is called degenerate calculation, and the result of power is called power, a is called basic telephone, and n 。

The mixing order is: multiply first, then multiply and divide, and finally calculate the first number of brackets.

2. Real irrational number: a transcendence is called irrational number.

Square root: ① If the square of a positive number X is equal to A, then X is the so-called positive square root (2) If the square of a number X is equal to A, then the number of X is called the square root of A. ③ It is a positive number, and the square root of 2/0 0/negative number. (4) The operation of finding the square root a of a number is called square root, and one of them is called square root.

Cubic root: ① If the cube root of a number X is equal to A, then the cube root of this number X is A2. The cube root of a positive number is positive and the cube root of a negative number is negative. ③ The cube root of the number calculated on demand is called the issuing bank and the other is called the issuing bank.

Real numbers: ① Real numbers are rational numbers and irrational numbers. (2) Real numbers, whose internal meanings are exactly the same as those of the inverse number, the absolute value of reciprocal and the absolute value of reciprocal in rational numbers. ③ The point on each real number line can be expressed as.

3. Algebraic expressions

Algebraic expression: It is a single number or letter in algebra.

Merge similar items: (1) Items with the same letters are called similar item indexes. ② Similar items are merged into a so-called merged similar item. By merging similar items, the coefficients of similar items are added to the letters, and the index of the letters remains unchanged.

4. Integral and Fraction

Beginning: ① The algebra of product is called monomial, and the so-called polynomial monomial and polynomial are collectively called the beginning numbers and letters. ② Call numbers of all letters and monomials in a single index. The number of terms in the polynomial of (3) is called the degree of the polynomial of a number.

Start operation: addition and subtraction. If the brackets are removed for the first time, similar items are merged.

Exponential operation: AM+AN = A(M+N)

(AM)N = AMN

A/B N = AN/BN department. about

Positive multiplication: ① The monomial is multiplied by letters with the same coefficient, and a power supply is multiplied separately, which is the same as the other letters, and together with his index, it is used as the factor of the product. (2) The multiplication of monomial and polynomial is the distribution law, and the sum of graphs generated by monomial and polynomial. (3) The polynomial and polynomial are multiplied by the first polynomial and the second polynomial respectively, and then the sum of the products is obtained.

Formula 2: Two Square Formulas/Perfect Way

Zheng's division: ① the coefficient of a single item divided by the same basic ability factor, the difference of division; For the case that the formula only contains letters, it is used as a supplier's factor together with its index. The polynomial of is divided by the first polynomial of the monomial, then divided by each monomial, and then the quotient sum of.

The beginning of decomposition into the form of numbers, the plot of this change: a polynomial is called the factorization of polynomials.

Methods: Common factor method, formula method, grouping decomposition method and cross multiplication method.

Fraction: ① Right at the beginning, A is divisible by Zheng's B. Except that the denominator in B is decimal, the denominator of any fraction is not 0. 2 the same? The numerator and denominator of the multiplication or division of the same fraction are not equal to 0, and the value of the initial fraction remains unchanged.

Score calculation:

Multiplication: Draw the numerator of the conspirator, and multiply the denominator by the product as the denominator of the product. about

Division: Divided by times, the reciprocal of a fraction is equal to a fraction.

Addition and subtraction: addition and subtraction of fractions with the same denominator, numerator and denominator. (2) The first * * * exclusive denominator score is the same denominator score, and then add and subtract.

Fractional formula: ① The unknown in denominator equation is called fractional formula. ② The denominator of the zero solution equation is called the root increment of the original equation.

B. Equality and inequality

1, equation and equation

Time equation: ① An equation contains only one unknown quantity, and the unknown quantity index is 1, then the equation is simple. ② Both sides of the equation are added or subtracted at the same time, or multiplied or divided by an algebraic expression (not 0), and the result is still an equation.

Steps to solve a linear equation with one variable: remove the denominator, exchange and merge similar terms, and the unknown coefficient is 1.

Linear equation: An equation called linear equation contains two unknowns and one unknown.

Linear equations: Two equations of two linear equations are called two sets of linear equations.

A set of unknown values of binary linear equations are called two solutions of linear equations.

Simple binary formula, the solution of common equations, this simple binary formula.

Solve two groups of linear equations: substitution elimination method/addition and subtraction elimination method.

Quadratic equation of one variable: an unknown coefficient equation with only one unknown term.

The quadratic function relation of 1) unary quadratic equation

We learned to use quadratic function (parabola), and he also has a deep understanding of solutions, images and so on. In fact, it is to express a quadratic equation and a quadratic function. In fact, a special case of quadratic function of quadratic equation of one variable is the quadratic equation of one variable formed when y 0. In rectangular coordinate system, if a quadratic equation is a quadratic function, the intersection of the image and the x axis. In other words, the solution of the system of equations

2) Solution of quadratic equation in one variable.

We all know the vertex of the quadratic function (-b/2a 4ac-b2/4a), so it is very important to remember it. For example, a quadratic equation with one variable is a part of the quadratic function, so he has a solution, and he can find it all in one equation.

With the formula (1), the equation becomes a perfect solution.

(2) Direct Kaiping Method

* * * same factor is extracted, and the coefficient method is decomposed by formula method and cross-phase multiplication. When solving a quadratic equation with one variable, the form of the equation is multiplied by the solution.

(3) Formula method

This method can also be used in the general method of solving a quadratic equation with one variable, where the root of the equation is X 1 = {-B +√ b2-4ac)]/2a, and X2 = {-β-√[ b2-4ac ]}/2a.

3) Step 2 of solving the equation:

(1) and each step of the method:

The first constant term is moved to the equation on the right, and then it reaches the coefficient 1 of the quadratic term, plus half the area of the coefficient 1 at the same time, and finally a complete square formula is matched.

(2) Method steps of decomposition:

The equation on the right hand side is zero. Then, let's see if we can use the * * * same factor method (factorization formula method here) or cross multiplication to extract the formula, which can reduce the form of the product.

(3) If we can put the formula method

The coefficient generation of the quadratic term of the coefficient unary quadratic equation is a long-term constant term coefficient b,?

4) Vieta theorem

Understanding of Vieta Theorem Vieta Theorem is two A =-B/A of a quadratic equation, and two products = C/A can also be expressed as the/of X 1+X2 =-b and the/Vieta Theorem of x1x2 = c/a. We can calculate the coefficients of a quadratic equation with one variable, usually in the topic.

5) the root of the unary equation

Using the discriminant of roots to understand the discriminant of roots can be written as "△" and read as "tune ta", which can be divided into three types:

I am △ > 0, the real number roots of unary quadratic equation 2 are not equal;

2. △= B2-4AC Here, when△ = 0, the quadratic equation of one variable has two identical real roots;

Sandang delta

Inequalities, inequalities and symbols of inequalities >, =,< are called inequality formulas. Both sides of the inequality (2) add and subtract a positive beginning, and the number of directions remains the same. ③ Both sides of inequality are multiplied or divided by a positive number, and the direction of inequality remains unchanged. ④ The inequality on both sides is multiplied by or divided by a negative sign inequality in the opposite direction.

Solution set: (1) The value of inequality is unknown, so-called inequality. (2) Unequal unknowns contain all solutions, and the composition of the solutions is set. This process is called solving ③ inequality.

The left and right sides of one-dimensional linear inequality are business, which contains only one unknown. The highest unknown is an inequality called one-dimensional linear inequality.

In a group: ① Several unknown inequalities have the same * * * and consist of a set of linear inequalities. ② 1 unary inequality, and the common part of the solution set of inequality is called the solution set of a set of linear inequalities. (3) Inequality in seeking the law.

Directional symbols of inequality:

One-dimensional linear inequality, the difference is that when you add or multiply, the equality sign changes the same.

Inequality, plus inequality of sign redirection of the same number (or positive number); For example: A>b, A+C > B + C

Unequal, if you use the same number, (or add a negative number), the unequal symbols will not be redirected, for example, A>b, AC> BC.

Unequal phenomena, if multiplied by the same positive number, will not become, for example: A>B, A * B * C(C>；; 0)

Inequality, if multiplied by the same negative number, is redirected from the first one, such as: a >；; b，A * C & ltb * C(C & lt； 0)

If the inequality is multiplied by 0, then the inequality is replaced by an equal sign.

Multiply the required number by the question, and then they will see if there is a unary inequality in the question. If there is, the inequality multiplied by the number is 0, otherwise the inequality is not established;

Three functions

Variables: dependent variables and independent variables.

The relationship between variables is represented by images, and the number of independent variables is usually dependent variables, which is represented by the number of axes in the horizontal direction and the number of axes in the vertical direction.

Function: ① If the relationship between two variables X and Y can be expressed as: Y = KX+B(B is a constant and K is not equal to 0), then Y is a function of linear X. ② When B = 0, Y is a direct function of the ratio X. ..

Primary image function: ① Independent variable X and dependent variable Y of the function correspond to abscissa and ordinate points respectively, and the corresponding points are defined in Cartesian coordinate system. The graphic image composed of all these points is called this function. ② Proportional function Y = KX The image is a straight line passing through the origin. (3) In the main function, when k

Space and graphics

Graphic understanding

Point, line and surface

Point, line and surface: ① a figure composed of points, lines and surfaces. (2) Lines intersecting face to face, and points where lines intersect. (3) Points form lines, lines form planes, and planes form bodies.

Unfolding and folding: ① Prism, the intersection of any two adjacent faces is called edge, the intersection of two sides adjacent to the side, and all the sides of the prism are displayed. The top and bottom of the prism have the same shape and are in the shape of the side of a cuboid. ② The prism on the N side of the neurotic prism base map.

Cutting the geometric plane cuts the figure, and the cutting plane is called "cross section".

Views: front view, left view, schematic view and plan view.

Polygons: Are they closed figures connected end to end on the same line segment?

Arc fan: ① called arc, and then the two endpoints on the graphics card take this arc as the radius fan. ② It can be divided into several fan-shaped circles.

2. Angle

Line: ① A line segment has two endpoints. (2) One direction of the ray segment formed by infinite extension. A ray has only one endpoint. ③ Endpoints of infinitely extending line segments to form a straight line. The endpoint of a straight line. ④ There is only one on two straight lines.

Compare the lengths of line segments: ① All the connecting lines between the shortest two points. The length of the line segment between two points ② is called the distance between these two points. about

Angle measurement: ① The angle between the vertex of two rays with the same angle as a * * * and the vertex of two rays in common * * *. ② Every 1/60 minutes, 1/60 seconds.

Angle comparison: ① The angle can also be seen from the left and right rotation of the light from its endpoint. (2) A ray rotates at its endpoint. When the last edge begins to form a straight line, the angle formed is called a straight angle. When the starting edge continues to rotate, the angle formed when it coincides with the starting edge is called a whole circle. The light from the vertex is divided into two equal angles, which is called the bisector of this angle.

Parallelism: ① Two straight lines that do not intersect in the same plane are called parallel lines. ② After a straight outer point, there is only one straight line parallel to it. If two lines are parallel to three lines, then the two lines are parallel to each other. about

Perpendicular: If two lines intersect at right angles, they are perpendicular to each other. The intersection of two vertical lines is called pedal ②. (3) There are too few planes, and only on a straight line can we know that they are perpendicular to the straight line.

A straight line in the middle vertical line: the vertical bisector is called the middle vertical line.

A line segment of the median vertical line, the median vertical line, must not be-ray, or be on a straight line. According to the ray and the line that can extend infinitely, the back of the middle vertical line can be a straight line, so when you decide after 2 o'clock, draw a clothes for the middle vertical line (draw and then say) and 2 o'clock.

Median vertical theorem: Yes.

Property theorem: the line segments of the two endpoints of the equidistant median vertical line;

The equidistant point of the endpoint of the second paragraph of the decision theorem is on the middle vertical line of this field.

Angular bisector: The angular bisector of an angle is called the angular bisector.

Definition, there are several points to pay attention to. Yes, is the bisector of the included angle a ray or a straight line segment? Many times, there will be a straight line in the topic, which is the bisector point.

Before the property on the same line, the symmetry axis of the bisector of an angle of the trajectory involved is equal to the distance between the angles on both sides of the bisector of the angle.

The decision theorem of: the distance between two sides is equal

Angle of bisector of a square in an angle: the quality of a group of rectangles with equal distances between adjacent sides.

All the properties of squares, parallelograms, diamonds and rectangles are

Judgment: The rhombus with equal diagonal lines is equal to the rectangle with adjacent sides.

Two basic theorems

There is only one straight line between the two directions.

2

Between the shortest two points in 3 paragraphs, the complementary angle is equal to the same angle or equal angle.

The complementary angle is equal to the same angle or equal angle, with a small straight line and a known vertical line.

The connection points and outer points of all straight line segments are on a straight line, and the vertical line segment is the shortest.

Parallel to the straight line after the axiom point, and only parallel to the straight line

On a straight line, if two straight lines are parallel to the third straight line, the two straight lines are parallel to each other.

9. The corresponding angles are all equal and the two straight lines are parallel.

10, the angle is not equal to two parallel rows.

1 1, which is complementary to the next inner corner and the two straight lines are parallel.

12, two straight lines are parallel, and the corresponding angles are equal to.

13, the error angle of two parallel lines is equal to

The two lines of 14 are parallel and complementary to the next inner corner.

15, theorem that the sum of two sides of a triangle is greater than the third side /> 16 Infers that the difference between two sides of a triangle is less than the third side.

17, the angle of a triangle and three angles are equal to 180.

18, the inference of two acute angles

19 infers that the outer angle of a triangle is equal to the interaction of a right triangle, which is two non-adjacent inner angles >; 20. It is inferred that the outer angle of a triangle is larger than any one, and it is a non-adjacent inner angle of 2 1, and the corresponding angles of the corresponding sides of congruent triangles are equal.

The included angle between two sides of 22 Angle Axiom (SAS) corresponds to the combination of two equal triangles.

23, he has two diagonal axioms (ASA) and congruences of two equilateral triangles.

The angle of inference (AAS) and an angle correspond to the congruence of two equal triangles.

25-sided axiom (SSS) The sides corresponding to three sides are congruent with two equal triangles.

26 hypotenuse, right angle axiom (HL), two hypotenuse are equal, and a right triangle with right angles on its sides is congruent.

27. Theorem 1 Equidistant points of angular bisector are on both sides of this angle.

28. Theorem 2- 1 The distance between two sides of an angle and a point is equal, and the angle bisector of the angle bisector.

29 is the equal distance between the angles on both sides of all points in the group.

30, the nature theorem of isosceles triangle The two bottom angles of an isosceles triangle are equal (equilateral).

3 1, inference 1 sum of the bisectors of the top angles of isosceles triangles bisecting the bottom edges? Perpendicular to the bottom edge

32. The midline and coincidence of the bisector of the top angle of the isosceles triangle.

Inference 3 The base of each angle of an equilateral triangle is equal, and one of each angle is equal to 60.

34 isosceles triangle judgment theorem If a triangle has two equal angles, then the two angles of the side are equal (equal angles and equal sides).

35. Inference triangles are all equal and triangles are regular triangles.

36. Inference 2 of an isosceles triangle has an angle equal to 60 that is a regular triangle.

37. In a right triangle, if an acute angle is equal to 30, half of the hypotenuse of the upper right corner is equal to.

38. The median line on the hypotenuse is a hypotenuse equal to half.

39. Theorem: The distance between the midpoint of the line segment and the two end points of the line segment is equal to/>; 40, against

4 1, a line segment whose distance from the midline of the line segment is equal to the midline of the two endpoints of the line segment can be regarded as all points whose distance from the line segment is equal to the two endpoints.

42. Theorem 1 The setting of two linearly symmetric graphs is the same shape.

43. Theorem 2 If two graphs are symmetrical about a straight line, the corresponding points of the perpendicular line in the axial symmetry are connected.

Theorem 3: Two linearly symmetric graphs are symmetric if their corresponding line segments or extension lines intersect, and then symmetric.

On the contrary, if the points corresponding to the intersections of axes of two graphs are connected on the same straight line, that is, the perpendicular bisector, 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-angled triangle is equal to the square of the hypotenuse, and A2+B2 = C2.

47. Pythagorean Theorem The three sides of an inverted triangle are A, B and C, and there is a relationship A2+B2 = C2, then the triangle is a right triangle.

48, the angle of the quadrilateral is equal to 360.

49, the sum of the external angles of the quadrilateral is equal to 360.

50. The sum of the angle of the polygon and the angle of the inner N-sided polygon is equal to (? -2)× 180

5 1, inferring that the external angle of any polygon is equal to 360.

52 parallelogram property theorem 1 parallelogram has equal angles.

53, parallelogram property theorem 2 parallelogram sides are equal

54 is equal to the reasoning sandwiched between two parallel lines and parallel line segments.

Parallelogram theorem of 55, properties of parallelogram, diagonal bisection.

56 parallelogram decision theorem 1 two groups of parallelograms with diagonal lines equal to quadrilaterals respectively.

57 Judgment Theorem of Parallelogram 2 Two groups of parallelograms with equal sides are parallelograms.

59. The decision theorem of parallelogram A set of four quadrilateral parallelograms.

58 Judgment Theorem of Parallelogram 3 Parallelogram with equal diagonal bisectors and opposite sides

60. Nature Theorem of Rectangle 1 All four corners of a rectangle are right angles.

6 1, rectangle property theorem 2

62. The diagonal of the rectangle is equal to the rectangle judgment theorem 1. There are three right-angled quadrangles in a rectangle.

Parallelogram Theorem of 63 Rectangle Judgment Two Rectangles with Equal Diagonal Lines

The diamond property theorem has equal diamonds on four sides.

65. Theorem 2 is about the perpendicular nature of rhombic diagonals and a set of angles of rhombic area bisected by each diagonal.

66 = line product of half diagonal, S =(A×B)÷2.

67 diamond decision theorem 1 quadrilateral diamond with four equal sides

68 Diamond Decision Theorem 2 Diamonds of parallelograms whose diagonals are perpendicular to each other

69. The square property theorem 1 is equal to the four sides of a right angle.

70. Theorem 2 of the square property of two diagonals is equal, and the perpendicular line of each diagonal bisects the diagonal.

7 1, theorem 1 Two symmetric graphs are congruent.

72. Theorem 2 Symmetries two figures, the symmetrical points are connected with central symmetry, and the central symmetry is bisected.

73. Connect the corresponding points of a certain point of two graphs in reverse, and the two graphs divided equally are symmetrical.

Property theorem that 74 equals isosceles trapezoid. An isosceles trapezoid is at two corners of the same base.

75. An isosceles trapezoid with two diagonal lines.

Judgement theorem of isosceles trapezoid Two isosceles trapezoid on the same base are isosceles trapezoid.

77. The diagonal is equal to the trapezoid, which is the isosceles trapezoid.

Theorem of bisecting line segments by parallel lines, if a group of parallel lines are equal on the cut line segments, the line segments cut by other lines are also equal.

79. It is inferred that the other waist should be bisected after the midpoint of 1 is parallel to the straight line of the trapezoidal waist bottom.

After inference 2, the midpoint of one side of the triangle and the straight line parallel to the other side will divide the third side equally.

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

82. Half of the two bases whose median lines are parallel to each other in the trapezoid theorem, the sum of the two bases is equal, and L =(A+B)÷2 S = L x is high.

83. The basic attribute of the ratio of (1): A: B = C: D, and then if AD = BC, AD = BC,: B = C: D.

84. (2) If the total performance of A/B is = C/D, then (A B)/B = (C D)/D.

85. (3) Geometric properties: A/B = C/D =...= M/N(B+D+...+n≠0 ≠ 0),

(A + C +...+ M)/(B + D +...+ N)= A / B

86. Parallel lines are piecewise proportional theorem 3 Two straight lines of parallel lines are proportional to the corresponding line segments obtained.

Infer the line segment ratio corresponding to two sides of the tangent (or triangle sides with parallel extension lines on both sides).

Theorem If the obtained straight line (or the two sides of the extension line of the corresponding line segment are proportional) is each leg of the cross section of a triangle, then this straight line is parallel to the third side of the triangle.

The sides of the triangle of 89 are parallel, and the three sides of the other triangles intersecting with the straight lines of the corresponding sides are directly proportional to the three sides of the original triangle >: 90. Theorem One side of a triangle is similar to the original triangle formed by the intersection of two parallel lines (or extension lines on both sides) on the other side.

9 1, similar triangles's theorem that the corresponding angles are equal and the two triangles are similar (ASA).

92. Divide into two right-angled triangles with hypotenuse and height similar to the original triangle.

93. Determine the similarity (SAS) of two triangles. Both sides of Theorem 2 of these two triangles are equal to the angle between the corresponding proportions.

94. Two triangles are similar (SSS) if the three sides of the hypotenuse judgment theorem of a right triangle have corresponding proportions.

95. Theorem The side of a right angle and the other hypotenuse correspond to the proportion of a right angle, so the two triangles are similar.

96. Theorem 1 similar triangles's properties, corresponding height ratio, and corresponding centerline ratio of angular bisector/>; Ratio 97 equals similarity theorem 2. The ratio of similar triangles perimeter is equal to the similarity ratio.

Is the area ratio of property theorem 3 similar? The similarity ratio of triangles is equal to squares.

99. Is the sine value of any acute angle equal to the cosine value of any acute angle of the remaining angles? Is the sine of the congruence angle.

100 The tangent of any acute angle is equal to the cotangent of the complementary angle, and any acute angle is equal to the tangent of the other angles.

10 1 Using the residual shear value, the distance between the circle and the point is set to the same length.

The interior of the circle of the set of 102 points can be regarded as the set of center points whose distance is less than the radius.

The outer side of the circle of 103 can be regarded as a collection of points whose center distance is greater than the radius.

104, the radius of the same circle or circle is equal to

The trajectory length of the point 105 set to a fixed distance is designated as the circle with the center radius.

106, the trajectory of the front pipe section of the median vertical line with a fixed length and the point whose distance is equal to the connecting line of two known endpoints.

107, the trajectory to the point with equal distance on both sides reaches a known angle and angle bisector.

108 point? The distance between two parallel lines of the trajectory is equal, and so is the distance between two parallel lines.

Is theorem 109 a circle that defines three points on the same straight line?

1 10, vertical diameter theorem, chord diameter bisects two arcs on the chord bisected by this chord vertically.

1 1 1 inference 1

(1) bisects the diameter of a chord (diameter) perpendicular to the chord, and perpendicular bisector bisects the chord into an arc.

(2) After the center of the chord, two arcs

(3) The bisecting chord perpendicular to the diameter of the arc bisects the chord bisects the chord and bisects the chord arc.

1 12 Inference 2 Another folder with two circles connected in series and parallel is equal arc.

1 13 center symmetry

1 14. In the same circle or circle theorem, the central angles of arcs on a circle are equal and equal to the chord centers.

1 15 By the same reasoning, the distance between the centers of two central angles, two arcs, two character strings or two character strings on the same circle or the same arc of a circle is equal to their corresponding equations.

1 16, the theorem is equal to the central angle on half of it.

1 17 The set values or arcs in the remaining components of the arc angle inferred from the arc are equal; Equal circumferential angles are on the same circle or circle, and the arc is equal to

1 18, it is inferred that the circumferential angle on the semicircle (or diameter) is a right angle, and the right chord with a circumferential angle of 90 is the diameter.

1 19 Inference 3 If the median line of the sides of a triangle is equal to half of the sides, then the triangle is a right triangle.

120 complementary angle theorem is inscribed with a quadrilateral, which is equal to any external angle and internal angle.

Line l ⊙ outside diameter

② straight line l and ⊙O D = R

(3) The correlation between the straight line L and ⊙O is d >; ?

122 The radius of the outer end after the tangent judgment theorem is tangent to the straight line perpendicular to this radius.

123 radius of tangent vertical point of tangent theorem of circle tangency

124 Infers that 1 crosses the center of the circle and is perpendicular to the tangent point of the tangent line.

125, inference 2 will pass through the tangent point and vertical tangent line and must pass through the circle.

The tangent length theorem 126 leads to the center of the second tangent from the outer circle, and the circle where the center is located is tangent, which seems to be the same two tangent angles.

127, the edge sum of two groups circumscribed by rounded rectangle.

128, Xi Anqie Angle Theorem Xi Anqie Angle is equal to the fillet on the arc.

129, it is inferred that if the arcs of two Xi Anqie angle folders are equal, then the two Xi Anqie angle folders are also equal.

130, two-cut chord theorem A circle cuts a chord, which is divided into two parts, and the intersection points are equal in length.

13 1, it is inferred that if the diameter of a chord is perpendicular to half the diameter of a chord, it is divided into two parts.

132, the tangent theorem leads to the tangent and secant of the circle, the length of the tangent, and the ratio of the two line segments at the intersection of the secant and the circle.

Item 133, from the circle of a point, infer the secant referenced outside the circle, that is, the product of the lengths of two lines intersected by each secant circle is equal to

134, the tangent point of two circles must even be the heart.

135① "D > of two circles; R+R2Two-loop nucleic acid exonuclease E = R+R+R② < D R)

④ tangent of circle D = RR(R string registration/> > R)⑤ The circle contains d R)

Theorem 136 The perpendicular bisector of the straight line of the center of two circles intersected by theorem 137 is divided into n (when n ≥ 3): BR/& gt；; (1) After the link is opened, the tangent polygon of the circle of each point (2) The inscribed circle of each point is a regular N polygon.

The polygon with the tangent vertex of adjacent intersection points is a circle, and the exonuclease of nucleic acid is positive N Kun.

Theorem 138 The inscribed circle of the circumscribed circle of any regular polygon is concentric.

139 every inner angle of a regular n-polygon is equal to (n-2) ×180/n.

140, it is proved that the radius of a regular N-polygon and the regular N-side in the center of the side form 2n congruent triangles.

14 1 the area of a regular n-polygon? SN = pnrn/2 P positive n-polygon perimeter

142 is described by √3a/4 of the long side of the equilateral triangle area.

The positive angles of an N-polygon whose vertex K is near 143, because these angles should be 360? K ×(n-2) 180/n = 360 to (n-2) (k-2)= 4.

144, arc length formula: L = Wu Zhi R/ 180.

145, fan area formula: s fan = N Wuri 360 = LR/2.

Common tangent in 146 = D(RR) tangent length = D-(R+R)W