The first day of the second book mathematical triangle knowledge points
I. Objectives and requirements
1. Know the triangle, know the meaning of the triangle, know the sides, internal angles and vertices of the triangle, and express the triangle in symbolic language.
2. Experience the practical activities of measuring the side length of a triangle and understand the unequal relationship among the three sides of the triangle.
3. Know how to judge whether three line segments can form a triangle, and use it to solve related problems.
4. The interior angle theorem of triangle can be deduced from the properties of parallel lines.
5. Some simple practical problems can be solved by applying the triangle interior angle sum theorem.
Second, the main points
Theorem of sum of interior angles of triangle;
In order to understand the concept of triangle, three bars can be expressed in symbolic language.
Third, difficulties.
The reasoning process of triangle interior angle sum theorem;
Identify all triangles without repetition or omission in specific graphics;
Judging whether three line segments can form a triangle by the unequal relationship of three sides of a triangle.
Fourth, the knowledge framework.
Verb (abbreviation of verb) summary of knowledge points and concepts
1. triangle: A figure composed of three line segments that are not on the same line and are connected end to end is called a triangle.
2. Classification of triangles
3. Trilateral relationship of triangle: the sum of any two sides of triangle is greater than the third side, and the difference between any two sides is less than the third side.
4. Height: Draw a vertical line from the vertex of the triangle to the line where the opposite side is located, and the line segment between the vertex and the vertical foot is called the height of the triangle.
5. midline: in a triangle, the line segment connecting the vertex and the midpoint of its opposite side is called the midline of the triangle.
6. Angular bisector: The bisector of the inner angle of a triangle intersects the opposite side of this angle, and the line segment between the intersection of the vertex and this angle is called the angular bisector of the triangle.
7. Significance and practice of high line, middle line and angle bisector.
8. Stability of triangle: The shape of triangle is fixed, and this property of triangle is called stability of triangle.
9. Theorem of the sum of interior angles of triangle: the sum of three interior angles of triangle is equal to 180.
It is inferred that the two acute angles of 1 right triangle are complementary;
Inference 2: One outer angle of a triangle is equal to the sum of two non-adjacent inner angles;
Inference 3: One outer angle of a triangle is larger than any inner angle that is not adjacent to it;
The sum of the inner angles of a triangle is half of the sum of the outer angles.
10. External angle of triangle: the included angle between one side of triangle and the extension line of the other side is called the external angle of triangle.
1 1. The Properties of the Exterior Angle of Triangle
(1) Vertex is the vertex of a triangle, one side is one side of the triangle, and the other side is the extension line of one side of the triangle;
(2) An outer angle of a triangle is equal to the sum of two inner angles that are not adjacent to it;
(3) The outer angle of a triangle is greater than any inner angle that is not adjacent to it;
(4) The sum of the external angles of the triangle is 360.
12. Polygon: On the plane, a figure composed of end-to-end line segments is called a polygon.
13. Interior angle of polygon: The angle formed by two adjacent sides of a polygon is called its interior angle.
14. Exterior angle of polygon: the angle formed by the extension line of one side of polygon and its adjacent side is called the exterior angle of polygon.
15. Diagonal line of polygon: the line segment connecting two non-adjacent vertices of polygon is called diagonal line of polygon.
16. Classification of polygons: it can be divided into convex polygons and concave polygons. Convex polygons can also be called plane polygons and concave polygons can also be called space polygons. Polygons can also be divided into regular polygons and non-regular polygons. Regular polygons have equal sides and equal internal angles.
17. Regular polygon: A polygon with equal angles and sides in a plane is called a regular polygon.
18. plane mosaic: covering a part of a plane with some non-overlapping polygons is called covering the plane with polygons.
Summary of mathematics knowledge points in grade one of junior high school
algebra
1. Algebraic expression: the expression of the number of connections, and the letters indicating this number with the operation symbol "+-×℉ ..." are called algebraic expressions. Note: There are certain restrictions on using letters to represent numbers. First, the number obtained by letters should ensure that its formula is meaningful; second, the number obtained by letters should also make it meaningful in real life or production; A single number or letter is also algebraic.
2. Some points for attention in column algebra (mathematical norms):
Multiply (1) by letters, or multiply letters by letters, or omit;
(2) When the numbers are multiplied, they should still be multiplied by "×", but not by "×", and the multiplication sign cannot be omitted;
(3) When a number is multiplied by a letter, the number is usually written in front of the letter in the result. For example, a×5 should be written as 5a;
(4) When the band fraction is multiplied by letters, the band fraction should be changed to a false fraction, for example, a× should be written as a;
(5) When there is a division operation in the algebraic expression, the division method and the division method are generally connected by a fractional line, such as the form written in 3 A;
(6) The difference between A and B should be written in alphabetical order; If we only talk about the difference between two numbers, when we set two numbers as A and B respectively, we should classify them and write them as a-b and B-A. 。
3. Several important algebraic expressions: (m and n represent integers)
(1) The square difference between A and B is: A2-B2; The square of the difference between a and b is: (a-b) 2;
(2) If a, b and c are positive integers, the two-digit integer is 10a+b and the three-digit integer is10a+10b+c;
(3) If both m and n are integers, the quotient m is divided by 5, and the remainder n is 5m+n; Even number is 2n, and odd number is 2n+1; Three consecutive integers are: n- 1, n, n+1;
(4) If b>0, positive number is: a2+b, negative number is: -a2-b, non-negative number is: a2, and non-positive number is: -a2.
The seventh grade mathematical formula daquan (next semester)
1 x number of shares per share = total number of shares ÷ number of shares = 2 1 multiple × multiple ÷ 1 multiple = multiple ÷ multiple = 1 multiple 3 speed × time = distance \
5 working efficiency × working time = total workload ÷ working efficiency = working time ÷ total workload ÷ working time = working efficiency 6 addend+addend = sum-one addend = another addend 7 minuend-subtree = difference minuend-difference = subtree+subtree = minuend 8 factor × factor = product ÷.
C perimeter s area a side length perimeter = side length ×4 C=4a
Area = side length × side length S=a×a 2 cubic v: volume a: side length surface area = side length× side length× ×6 S Table =a×a×6
Volume = side length × side length × side length V=a×a×a 3 rectangle
C perimeter s area A side length perimeter = (length+width) ×2 C=2(a+b) area = length× width S=ab 4 cuboid
V: volume s: area a: length b: width h: height (1) surface area (length× width+length× height+width× height )× 2s = 2 (AB+AH+BH) (2) volume = length× width× height V=abh 5 triangle S area A bottom H high area.
Triangle height = area × 2 ÷ base Triangle base = area× 2 ÷ height 6 parallelogram S area A base H height area = base× height s=ah 7 trapezoid
S area A upper bottom B lower bottom H height area = (upper bottom+lower bottom) × height ÷2 s=(a+b)× h÷2 8 circle.
S area c perimeter ∏ d= diameter r= radius (1) perimeter = diameter x ∏ = 2 x ∏× radius c = ∏ d = 2 ∏ r.
(2) Cylinder with area = radius × radius ×∏ 9
V: volume h: height s; Bottom area r: bottom radius c: bottom perimeter
(1) lateral area = perimeter of bottom× height (2) surface area = lateral area+bottom area× 2 (3) volume = bottom area× height (4) volume = lateral area ÷2× cone with radius of 10.
V: volume h: height s; Bottom area r: bottom radius
Volume = bottom area × height ÷3 Total number ÷ Total number of copies = formula (sum+difference) ÷2= large number (sum-difference) ÷2= decimal and multiple problems.
Articles related to important knowledge points in the second volume of junior one mathematics;
★ Summary of basic knowledge points in the second volume of junior high school mathematics
★ Summary of knowledge points in the second volume of junior high school mathematics
★ Summarize the knowledge points in the second volume of Mathematics in Grade One.
★ Summary of Key Knowledge Points of Mathematics in Volume 2 of Grade 1.
★ Summary of mathematics knowledge points in the next period of senior one.
★ Knowledge points of next semester in senior one mathematics.
★ Summary of mathematics knowledge points in the second volume of senior one.
★ Summary of seventh grade mathematics knowledge points
★ Summarize and sort out the knowledge points of Grade One mathematics.