Summary of Mathematics Knowledge Points in Senior Three I. Straight lines, intersecting lines and parallel lines
1. Differences and connections between line segments, rays and straight lines
This paper analyzes the graph, representation, boundary, number of endpoints and basic properties.
2. The midpoint of the line segment and its representation
3. Basic properties of straight lines and line segments (using the basic properties of line segments to prove that the sum of two sides of a triangle is greater than the third side)
4. The distance between two points (three distances: point-point; Dotted line; Line-line)
5. Angle (flat angle, rounded corner, right angle, acute angle, obtuse angle)
6. Complementary angle, complementary angle and their expressions
7. The bisector of an angle and its representation
8. Vertical line and its basic properties (use it to prove that the hypotenuse of a right triangle is larger than the right side)
9. Vertex angle and its properties
10. Parallel lines and their judgments and properties (reciprocal) (differences and connections between them)
1 1. Common theorems: ① parallel to two straight lines and parallel to one straight line (transitivity); ② Two straight lines parallel to and perpendicular to a straight line.
12. Definition, proposition and composition of proposition
13. Axioms and theorems
14. Inverse proposition
Second, the triangle
Classification: (1) Classification by edge;
(2) according to the angle.
1. Definition (including internal angle and external angle)
2. Relationship between angles of triangle: ⑴ Angle and angle :⑴Sum and inference of internal angles; ② sum of external angles; (3) the sum of the internal angles of the N-polygon; (4) the sum of the external angles of the N-polygon. ⑵ Edge and edge: The sum of two sides of a triangle is greater than the third side, and the difference between the two sides is less than the third side. ⑶ Angle and edge: In the same triangle,
3. The main part of the triangle
Discussion: ① Define ② the intersection of straight lines-the heart of triangle ③ property.
① High line ② Middle line ③ Angle bisector ④ Middle vertical line ⑤ Middle line.
⑵ General triangle ⑵ Special triangle: right triangle, isosceles triangle and equilateral triangle.
4. Determination and properties of special triangles (right triangle, isosceles triangle, equilateral triangle and isosceles right triangle)
5. congruent triangles
(1) Determine the consistency of general triangles (SAS, ASA, AAS, SSS).
⑵ Determination of congruence of special triangle: ① General method ② Special method.
6. Area of triangle
⑴ General calculation formula ⑴ Properties: The areas of triangles with equal bases and equal heights are equal.
7. Important auxiliary lines
(1) The midpoint and the midpoint form the midline; (2) Double the center line; (3) Add auxiliary parallel lines
8. Proof method
(1) direct proof method: synthesis method and analysis method.
(2) Indirect proof-reduction to absurdity: ① Counterhypothesis ② Reduction to absurdity ③ Conclusion.
(3) Prove that line segments are equal and angles are equal, often by proving triangle congruence.
(4) Prove the folding relationship of line segments: folding method and folding method.
5. Prove the sum-difference relationship of line segments: continuation method and truncation method.
[6] Prove the area relationship: indicate the area.
Third, quadrilateral.
Classification table:
1. General Properties (Angle)
(1) sum of internal angles: 360.
(2) Parallelogram connecting the midpoint of each side in turn.
Inference 1: Connect the midpoints of the sides of the quadrilateral in turn with equal diagonal lines to get a diamond.
Inference 2: Connect the midpoints of the sides of quadrangles whose diagonals are perpendicular to each other in turn to get a rectangle.
⑶ Sum of external angles: 360
2. Special quadrilateral
(1) General methods to study them:
(2) parallelogram, rectangle, diamond and square; Definition, properties and judgment of trapezoid and isosceles trapezoid
(3) judging step: quadrilateral parallelogram rectangle square
(4) diagonal tie rod:
3. Symmetric graphics
(1) axis symmetry (definition and properties); (2) Central symmetry (definition and nature)
4. Related Theorems: ① Parallel bisection theorem and its inference 1, 2.
② The midline theorem of triangle and trapezoid.
③ The distance between parallel lines is equal everywhere. (For example, find triangles with equal areas in the figure below)
5. Important auxiliary lines: ① Diagonal lines of quadrangles are often connected; ② In a trapezoid, a waist is often translated, and a diagonal line is translated to make a height. A vertex is connected with the midpoint of the waist, and the intersection with the bottom is extended, which is transformed into a triangle.
6. Drawing: Divide the line segments randomly.
The third grade mathematics knowledge point induction encyclopedia Chapter IV Linearity
★ Emphasis★ Concepts, judgments and properties of intersecting lines and parallel lines, triangles and quadrangles.
☆ Summary ☆
I. Straight lines, intersecting lines and parallel lines
1. Differences and connections between line segments, rays and straight lines
This paper analyzes the graph, representation, boundary, number of endpoints and basic properties.
2. The midpoint of the line segment and its representation
3. Basic properties of straight lines and line segments (using "basic properties of line segments" to demonstrate that "the sum of two sides of a triangle is greater than the third side")
4. The distance between two points (three distances: point-point; Dotted line; Line-line)
5. Angle (flat angle, rounded corner, right angle, acute angle, obtuse angle)
6. Complementary angle, complementary angle and their expressions
7. The bisector of an angle and its representation
8. Vertical line and its basic properties (use it to prove that "the hypotenuse of a right triangle is greater than the right")
9. Vertex angle and its properties
10. Parallel lines and their judgments and properties (reciprocal) (differences and connections between them)
1 1. Common theorems: ① parallel to two straight lines and parallel to one straight line (transitivity); ② Two straight lines parallel to and perpendicular to a straight line.
12. Definition, proposition and composition of proposition
13. Axioms and theorems
14. Inverse proposition
Second, the triangle
Classification: (1) Classification by edge;
(2) according to the angle.
1. Definition (including internal angle and external angle)
2. Relationship between angles of triangle: ⑴ Angle and angle :⑴Sum and inference of internal angles; ② sum of external angles; (3) the sum of the internal angles of the N-polygon; (4) the sum of the external angles of the N-polygon. ⑵ Edge and edge: The sum of two sides of a triangle is greater than the third side, and the difference between the two sides is less than the third side. ⑶ Angle and edge: In the same triangle,
3. The main part of the triangle
Discussion: ① Define the intersection of ② _ _ lines-the property of triangle× center ③.
① High line ② Middle line ③ Angle bisector ④ Middle vertical line ⑤ Middle line.
⑵ General triangle ⑵ Special triangle: right triangle, isosceles triangle and equilateral triangle.
4. Determination and properties of special triangles (right triangle, isosceles triangle, equilateral triangle and isosceles right triangle)
5. congruent triangles
(1) Determine the consistency of general triangles (SAS, ASA, AAS, SSS).
⑵ Determination of congruence of special triangle: ① General method ② Special method.
6. Area of triangle
⑴ General calculation formula ⑴ Properties: The areas of triangles with equal bases and equal heights are equal.
7. Important auxiliary lines
(1) The midpoint and the midpoint form the midline; (2) Double the center line; (3) Add auxiliary parallel lines
8. Proof method
(1) direct proof method: synthesis method and analysis method.
(2) Indirect proof-reduction to absurdity: ① Counterhypothesis ② Reduction to absurdity ③ Conclusion.
(3) Prove that line segments are equal and angles are equal, often by proving triangle congruence.
(4) Prove the folding relationship of line segments: folding method and folding method.
5. Prove the sum-difference relationship of line segments: continuation method and truncation method.
[6] Prove the area relationship: indicate the area.
Third, quadrilateral.
Classification table:
1. General Properties (Angle)
⑴ Sum of internal angles: 360.
(2) Parallelogram connecting the midpoint of each side in turn.
Inference 1: Connect the midpoints of the sides of the quadrilateral in turn with equal diagonal lines to get a diamond.
Inference 2: Connect the midpoints of the sides of the quadrilateral in turn with diagonal lines perpendicular to each other to get a rectangle.
⑶ Sum of external angles: 360.
2. Special quadrilateral
(1) General methods to study them:
(2) parallelogram, rectangle, diamond and square; Definition, properties and judgment of trapezoid and isosceles trapezoid
⑶ Determination steps: quadrilateral → parallelogram → rectangle → square.
┗→ Diamonds-=
(4) diagonal tie rod:
3. Symmetric graphics
(1) axis symmetry (definition and properties); (2) Central symmetry (definition and nature)
4. Related Theorems: ① Parallel bisection theorem and its inference 1, 2.
② The midline theorem of triangle and trapezoid.
③ The distance between parallel lines is equal everywhere. (For example, find triangles with equal areas in the figure below)
5. Important auxiliary lines: ① Diagonal lines of quadrangles are often connected; ② Trapezoids are often transformed into triangles by translating a waist, translating a diagonal, making a height, connecting the midpoint between the vertex and the waist and extending the intersection with the bottom.
6. Drawing: Divide the line segments randomly.
Junior high school mathematics knowledge points are summarized in algebra: rational number, irrational number, real algebraic expression, fraction, quadratic root linear equation, quadratic equation, quadratic equation, fractional equation, linear inequality function (linear function, quadratic function, inverse proportional function).
Geometric part: line segment, intersection line, parallel triangle, quadrilateral, similar shape, circle.
1, classification of real numbers
Rational Numbers: Integers (including positive integers, 0 and negative integers) and fractions (including finite decimals and infinite cyclic decimals) are rational numbers. Such as:-3,0.231,0.7773 ...
Irrational number: Infinitely circulating decimals are called irrational numbers, such as π,-,0. 1 0 1 001... (between two1,there are1zeros in turn).
Real numbers: Rational numbers and irrational numbers are collectively called real numbers.
2. Irrational number
When understanding irrational numbers, we should grasp the moment of "infinite acyclic", which contains two meanings: one is infinite decimal; Second, it does not circulate. Both are indispensable. To sum up, there are four categories:
(1) An inexhaustible number, such as;
(2) Numbers with specific meanings, such as pi, or simplified numbers with pi, such as+8;
(3) Numbers with specific structures, such as 0.101001001...;
(4) some trigonometric functions, such as sin60o, etc.
Note: To judge the attributes of a real number (such as rational number and irrational number), the following principles should be followed: simplification, discrimination and judgment. It should be noted that neither "spiritual similarity" nor "formal similarity" can be used as a criterion for judgment.
3. Non-negative number: the collective name of positive real number and zero. (Table: x≥0)
Common non-negative numbers are:
Property: If the sum of several non-negative numbers is 0, then every unburdened number is 0.
4. Number axis: The straight line defining the origin, positive direction and unit length is called the number axis (it should be noted that the above three elements are indispensable when drawing the number axis).
When solving problems, we should really master the idea of combining numbers with shapes, understand the one-to-one correspondence between real numbers and points on the number axis, and use them flexibly.
(1) Draw a horizontal straight line, take a point on the straight line to represent 0 (origin), choose a certain length as the unit length, and specify the right direction on the straight line as the positive direction to get the number axis ("three elements").
② Any rational number can be represented by a point on the number axis.
(3) If two numbers differ only in sign, then we call one of them the inverse of the other number, and we also call these two numbers the inverse of each other.
Function: a. Visually compare the sizes of real numbers; B. clearly reflect the absolute value; C. establish a one-to-one correspondence between points and real numbers.
5. Inverse number
A real number and its inverse are a pair of numbers (only two numbers with different signs are called inverse numbers, and the inverse of zero is zero). Seen from the number axis, the points corresponding to two opposite numbers are symmetrical about the origin. If a and b are opposites, then a+b=0, a=-b, and vice versa.
That is, the reciprocal of (1) real number is.
The knowledge points of senior three mathematics are summarized in the related articles of People's Education Press.
★ Summary of ninth grade mathematics knowledge points in People's Education Edition
★ Review materials of mathematics knowledge in senior high school entrance examination of PEP.
★ Summary of junior high school mathematics knowledge points
★ People's Education Edition Compulsory 3 Mathematical Algorithm Preliminary Knowledge Point Induction
★ Summary of knowledge points in the first volume of eighth grade mathematics published by People's Education Press
★ People's Education Edition, Grade One Mathematics, Book Two, review and summarize knowledge points, and prepare for the senior high school entrance examination.
★ People's Education Edition Ninth Grade History Volume II Knowledge Point Induction
★ Summary of Mathematics Knowledge Points in Senior Three of People's Education Edition
★ People's Education Edition must test the knowledge points of mathematics in senior three.
★ Knowledge points of the second volume of the third grade mathematics of People's Education Edition
var _ HMT = _ HMT | |[]； (function(){ var hm = document . createelement(" script ")； hm.src = "/hm.js？ 3b 57837d 30 f 874 be 5607 a 657 c 67 1896 b "； var s = document . getelementsbytagname(" script ")[0]； s.parentNode.insertBefore(hm，s)； })();