1. Consistency: Two drawings with the same shape and size can completely overlap.
Congruent triangles: Two triangles that can completely overlap.
Second, the main points
1. Graphic congruence before and after translation, folding and rotation.
2. The nature of congruent triangles: congruent triangles has equal sides and congruent triangles has equal angles.
3. congruent triangles's judgment:
Three sides of SSS correspond to two equal triangles.
The two sides of SAS and their included angles correspond to the congruent sides of two triangles.
The two corners of ASA and their clamping edges correspond to two equal triangle congruent angles.
The two corners of AAS and the opposite side of one of them open two equilateral triangles.
The hypotenuse and a right angle of HL correspond to the congruent hypotenuse and right angle of two equal triangles.
4. The nature of the angular bisector: the distance from the point on the angular bisector to both sides of the angle is equal.
5. Determination of the bisector of the angle: the points with the same distance from the inside of the angle to both sides of the angle are on the bisector of the angle.
Analysis of congruent triangles's knowledge points, the first volume of eighth grade mathematics 2 congruent triangles
Definition: Two triangles that can completely coincide are called congruent triangles.
Understanding: ① The shape and size of congruent triangles are completely equal, regardless of location;
② A triangle can be translated, folded and rotated to get its congruence;
③ The congruence of triangle does not change with the change of position.
Through the explanation and study of congruent triangles's knowledge points, I believe that students have mastered congruent triangles's knowledge well, and we will consolidate more knowledge points later.
Summary of junior high school mathematics knowledge points: plane rectangular coordinate system
The following is the study of the content of plane rectangular coordinate system. I hope students can master the following content well.
Cartesian coordinates/Cartesian coordinates
Plane Cartesian coordinate system: Draw two mutually perpendicular number axes with coincident origin on the plane to form a plane Cartesian coordinate system.
The horizontal axis is called X axis or horizontal axis, the vertical axis is called Y axis or vertical axis, and the intersection of the two coordinate axes is the origin of the plane rectangular coordinate system.
Elements of a plane rectangular coordinate system: ① On the same plane; ② Two axes of numbers are perpendicular to each other; ④ The origin coincides.
Three rules:
① The specified positive direction: the horizontal axis is right, and the vertical axis is oriented in the positive direction.
(2) the provisions of the unit length; Generally speaking, the unit length of the horizontal axis and the vertical axis is the same; In fact, sometimes it can be different, but it must be on the same axis.
③ Quadrant definition: the upper right is the first quadrant, the upper left is the second quadrant, the lower left is the third quadrant, and the lower right is the fourth quadrant.
I believe that the students have mastered the knowledge of plane rectangular coordinate system, and I hope they can all be admitted.
Knowledge points of junior high school mathematics: the composition of plane rectangular coordinate system
Let's learn about the composition of the plane rectangular coordinate system.
Composition of plane rectangular coordinate system
Two number axes perpendicular to each other on the same plane and having a common origin form a plane rectangular coordinate system, which is called rectangular coordinate system for short. Usually, the two number axes are placed in the horizontal position and the vertical position respectively, and the right and upward directions are the positive directions of the two number axes respectively. The horizontal axis is called X axis or horizontal axis, the vertical axis is called Y axis or vertical axis, and the X axis or Y axis is collectively called coordinate axis, and their common origin O is called the origin of rectangular coordinate system.
Through the explanation and study of the composition knowledge of plane rectangular coordinate system, I hope students can master the above contents well and study hard.
Junior high school mathematics knowledge points: the nature of the coordinates of points
The following is a study on the coordinate properties of points in mathematics. Students should take a closer look.
Properties of point coordinates
After establishing the plane rectangular coordinate system, we can determine its coordinates at any point on the coordinate system plane. Conversely, for any coordinate, we can determine a point it represents on the coordinate plane.
For any point C on the plane, the intersection point C is perpendicular to the X-axis and Y-axis respectively, and the corresponding points A and B perpendicular to the X-axis and Y-axis are respectively called the abscissa and ordinate of the point C, and the ordered real number pairs (A, B) are called the coordinates of the point C. ..
A point is in different quadrants or coordinate axes, and its coordinates are different.
I hope that the students can master the knowledge of the above coordinate nature, and I believe that the students will achieve excellent results in the exam.
Knowledge points of junior high school mathematics: general steps of factorization
About the general steps of factorization in mathematics, we will explain the following knowledge.
General steps of factorization
If the polynomial has a common factor, first mention the common factor, and then consider the formula method if there is no common factor. If it is a polynomial with four or more terms,
Usually, the group decomposition method is used, and finally the cross multiplication factor is used to decompose the factors. So it can be summarized as "one mention", "two sets", "three groups" and "forty words".
Note: Factorization must be decomposed until each factor can no longer be decomposed, otherwise it is incomplete factorization. If the topic does not clearly indicate the scope of factorization, it should refer to factorization within rational numbers, so the result of factorization must be the product of several algebraic expressions.
I believe the students have mastered the general steps of factorization, and I hope they will do well in the exam.
Knowledge points of junior high school mathematics: factorization
The following is the knowledge explanation of factorization in mathematics. I hope the students will study hard.
factoring
Definition of factorization: transforming a polynomial into the product of several algebraic expressions is called factorization of this polynomial.
Factorizing elements: ① The result must be an algebraic expression ② The result must be a product ③ The result is an equation ④.
The relationship between factorization and algebraic expression multiplication: m(a+b+c)
Common factor: The common factor of each term of a polynomial is called the common factor of each term of this polynomial.
Determination of common factor: ① When the coefficient is an integer, take the greatest common factor of each term. The product of the greatest common divisor of the same letter and the lowest power of the same letter is the common factor of this polynomial.
To select a common factor:
① Determine the common factor. ② Determine the quotient formula ③ The common factor formula and the quotient formula are written in the form of product.
Factorizing attention;
(1) Lost letters are not allowed.
(2) It is not allowed to lose the same items. Please check the quantity of items.
③ Change the double brackets into single brackets.
(4) The results are arranged in the order of number, single letter and single polynomial.
⑤ The same factor is written as a power.
⑥ The first minus sign is placed outside the brackets.
⑦ Similar items in brackets are merged.
Analysis of congruent triangles's knowledge points in the first volume of eighth grade mathematics III. Determination of triangle congruence
1. Three groups of congruences of two triangles with equal sides.
2. Two congruent triangles with two sides and an equal included angle.
3. The congruence (ASA) of two triangles with two angles and corresponding equal sides.
4. The opposite side with two angles and one angle corresponds to the congruence (AAS) of two triangles.
5. The congruence conditions of right-angled triangles are as follows: the hypotenuse and right-angled side correspond to the congruence of two right-angled triangles (HL).
Second, the nature of congruent triangles
1. The corresponding edges of congruent triangles are equal; Congruent triangles's corresponding angles are equal.
2. The circumference and area of congruent triangles are equal.
3. The heights of the corresponding sides of congruent triangles are equal.
4. The bisectors of the corresponding angles of congruent triangles are equal.
5. The median lines of the corresponding sides of congruent triangles are equal.
Third, the method of seeking congruent triangles
(1) It can be seen from the conclusion that which two possible congruent triangles are two line segments (or angles) to prove equality.
(2) We can determine which two triangles are equal from the known conditions.
(3) Considering the conditions and conclusions comprehensively, we can see that they can determine which two triangles are congruent;
(4) If all the above methods fail, we can consider adding auxiliary lines to construct congruent triangles.
The proof of triangle congruence contains two elements: edge and angle.
Four, the common methods of constructing auxiliary lines
About the auxiliary line of the angle bisector: when the angle bisector appears in the condition of the topic, we should think of constructing the auxiliary line according to the properties of the angle bisector.
The angular bisector has two properties: ① the angular bisector is symmetrical; ② The point on the bisector of the angle is equal to the distance on both sides of the angle.
Mathematical undetermined coefficient method
When solving mathematical problems, it is first judged that the obtained results have a certain form, which contains some undetermined coefficients, then the equations about undetermined coefficients are listed according to the problem setting conditions, and finally the values of these undetermined coefficients or some relationship between these undetermined coefficients are found. This method is called undetermined coefficient method to solve mathematical problems. It is one of the commonly used methods in middle school mathematics.
What is the advantage in mathematics?
A strip-shaped projection on an object, or a part where two planes in different directions are connected. Prism is a common three-dimensional polyhedron in geometry, which refers to a closed geometry with parallel and congruent upper and lower bottoms and parallel and equal sides. Cubes and cuboids have 12 side lengths, and different geometric shapes have different characteristics.