Seven-grade mathematics knowledge points
A preliminary understanding of graphics
Knowledge network:
Concept, definition:
1, we call all kinds of abstract figures in objects geometric figures.
2. Some geometric figures (such as cuboids, cubes, cylinders, cones, spheres, etc.). ) are not on the same plane, they are three-dimensional figures.
3. Some geometric figures (such as line segments, angles, triangles, rectangles, circles, etc.). ) are all in the same plane, which is a plane figure.
4. When the surface of the three-dimensional figure surrounded by the plane figure is properly cut, it can be expanded into a plane figure, which is called the expanded figure (net) of the corresponding three-dimensional figure.
5. Geometry is referred to as three-dimensional.
6. Surrounding the body is a curved surface, which has two kinds: plane and curved surface.
7. The intersection of surfaces forms a line, and the intersection of lines is a point.
8. Points move into faces, faces move into lines, and lines move into bodies.
9. After exploration, we can get a basic fact: there is a straight line after two points, and there is only one straight line.
Simply put, two points determine a straight line (axiom).
10, when two different straight lines have a common point, we call these two straight lines intersection, and this common point is called their intersection.
1 1, the point m divides the line segment AB into two equal line segments AM and MB, and the point m is called the center of the line segment AB.
12. After comparison, we can get a basic fact about the line segment: the line segment is the shortest of all two points. To put it simply: between two points, the line segment is the shortest. (axiom)
13, the length of the line segment connecting two points is called the distance between these two points.
14 and ∞ (angles are also basic geometric figures.
15, divide a fillet into 360 equal parts, and each equal part is an angle of 1 degree, which is recorded as1; Divide an angle of one degree into 60 equal parts, each part is called an angle of 1 minute, and it is recorded as1'; Divide the angle of 1 into 60 equal parts, and each part is called 1 sec, and it is recorded as 1 ".
16, starting from the vertex of an angle, the ray that divides this angle into two equal angles is called the angle bisector of this angle.
17, if the sum of two angles is equal to 90 (right angle), that is to say, the two angles are complementary.
Angle), that is, each angle is the complementary angle of another angle.
18, if the sum of the two angles is equal to 180 (flat angle), it is said that the two angles are complementary.
Angle), that is, one of the angles is the complement of the other.
19, the complementary angles of equal angles are equal, and the complementary angles of equal angles are equal.
Summary of mathematics knowledge points in grade one of junior high school
intersection line
One vertex has a common * * *, one side has a common * * *, and the other side is an extension line opposite to each other. Such two angles are called adjacent complementary angles.
There are four pairs of adjacent complementary angles when two straight lines intersect.
There is a vertex with a common * * *, and both sides of the corner are opposite extension lines. These two angles are called antipodal angles.
Two straight lines intersect and have two opposite angles.
The vertex angles are equal.
Two straight lines intersect, and one of the four corners is a right angle, so the two straight lines are perpendicular to each other. One of the straight lines is called the perpendicular of the other straight line, and their intersection point is called the vertical foot.
Parallel lines and their determination
Property 1: Two straight lines are parallel and equal to the complementary angle.
Property 2: Two straight lines are parallel and the internal dislocation angles are equal.
Property 3: Two straight lines are parallel and complementary.
Properties of parallel lines
Property 1 Two parallel lines are cut by a third line, and the congruence angles are equal. To put it simply: two straight lines are parallel and have the same angle.
Property 2 Two parallel lines are cut by a third straight line, and their internal angles are equal. To put it simply: two straight lines are parallel and their internal angles are equal.
Property 3 Two parallel lines are cut by a third straight line and complement each other. Simply put, two straight lines are parallel and complementary.
translate
Translate one unit length to the left and you can get the corresponding point (x-a, y).
Translate b unit lengths upwards, and you can get the corresponding point (x, y+b).
By translating down by b unit lengths, the corresponding point (x, y-b) can be obtained.
Review method of mathematics in grade one of junior high school
1 Return to books, organize chapters, conceptual formulas, property theorems, etc.
Just like building a house, whether the foundation of the house is solid or not. For example, in the review class, we ask our children to recite formulas, concepts such as monomials, polynomials and algebras, as well as the operation of powers and the multiplication and division of algebras. We must remember the square difference, complete square formula and deformation. Some children can memorize the complete square formula, but once they use it, they just don't need it. Because I am not skilled enough, I am afraid of making mistakes, so I use the most complicated formula to deduce it again, which is time-consuming and laborious, and always makes mistakes, and important formulas are even more unfamiliar.
For example, fill in the blanks with knowledge points:
Fill in the blanks with knowledge points
Our children usually do a lot of big questions at school and get some points in the exam, but they make mistakes in choosing to fill in the blanks. After the exam, they tried to watch it. The mistake is that the concept is unclear.
For example, how to define parallel lines, how many property theorems and how many judgment theorems are there? What are the connections and differences between them? In this chapter, where must we add the words "in the same plane"? Parents can let their children look for it.
For another example, the chapter of triangle involves the relationship between three sides and angles, as well as the important line segments of triangle and their properties, and the properties of isosceles equilateral triangle. These are definitely alternatives to the final multiple-choice question.
There are several ways to prove congruence, and the common auxiliary line method is the idea of geometric proof.
2. Break through the questions and summarize and practice the common hot issues in each chapter.
Our science subjects, such as mathematics and physics, are all about problems, not just problems. We must understand our thoughts.
You must analyze the types and difficulties of most children's exams, daily school assignments and weekly papers. You can mark the questions with different pens. For example, are questions 2 and 8 a kind of question type, a simplified evaluation or a deformed application of the formula? Through this analysis, children will find that in fact, exams are repeated practice. This is a very efficient learning method.
3. Familiar with routines and patterns
Common models of parallel lines: pencil model, trotter model, for example, I often tell you that parallel lines will be made when you meet an inflection point.
The common types of triangular chamfering are: 8-shaped, dart-shaped and angle-folded.
Triangle congruence model: natural model of angular bisector, isosceles right triangle model, three vertical model, folding (symmetry).
Learning these models well is equivalent to taking a toolbox exam, which is very efficient. Compared with other students, it saves the process of derivation and is fast and accurate. Of course, the premise is to master the basic content and not put the cart before the horse.
If the child can do all the previous steps well, master the basic knowledge points and questions, and can't make mistakes in calculation, then there must be no problem in your exam, except that some schools originally required it to be difficult, such as the finale, which is not to do too much, but to refine it. After finishing, continue to repeat the exam, say your thoughts in your own language and find out the logical relationship inside.
4. Insist on correcting the wrong questions
Bind the test papers of the whole semester together, spend half a day every week, correct the wrong questions, mark them with asterisks, and ask the teachers and classmates until they know, and continue to correct them next week to see if they really understand. For wrong questions, just like camels eating grass, children need to look at their ideas repeatedly to avoid repeating the mistakes of the same type of questions in the exam.
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