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How to learn the parallelogram of eighth grade mathematics well
The important geometric figure that senior two came into contact with in the first semester was triangle. After that, students focused on the knowledge of triangle congruence. By the second semester of Grade Two, the students of Grade Two had already learned the quadrilateral chapter. This chapter is the focus of geometry in Grade Two, which should attract the attention of all students. To learn this chapter well, we must first learn the parallelogram in the first section. Many students feel that they can't start when they are beginners of parallelogram. In view of this problem, give the students the following two suggestions: 1. Make good use of mathematical thinking methods. Mathematical thinking is called the "soul" of mathematics, and it is also the guiding ideology for learning mathematics and solving mathematical problems. The concrete implementation of mathematical thinking is realized by mathematical methods, and the two complement each other and are inseparable. The most commonly used mathematical thinking method for learning parallelogram is the transformation of numbers. Through the definition of parallelogram, we naturally associate the knowledge of parallel lines, that is to say, some new knowledge of parallelogram can be transformed into old knowledge of parallel lines. For example, using the property theorem of parallel lines "two straight lines are parallel and their internal angles are complementary", we can deduce an important property theorem of parallelogram "the diagonals of parallelogram are equal". If we sum up the geometry knowledge we have learned before into two pieces of knowledge, that is, straight lines and triangles. If we want to further study parallelogram, we must rely on the knowledge of triangle. How to realize the transformation between old and new knowledge? We can use the diagonal method. If a line is added, the parallelogram will be divided into two congruent triangles, which can prove the second property theorem of parallelogram, "The opposite sides of parallelogram are equal". If two diagonal lines are added to divide the parallelogram into four basic triangles, and the two equal ones are congruent respectively, we can prove the third property theorem of parallelogram, "the diagonal lines of parallelogram are equal". Therefore, the diagonal becomes an important auxiliary line to solve the parallelogram problem. This reformed mathematical thinking method can not only deduce new theorems, but also solve other problems. Second, the angle of finding the right knowledge is the same as what we learned before, because we learned the definition and then studied its nature and judgment. However, due to the particularity of parallelogram, when we study its property theorem and judgment method, we mainly analyze it from three different angles: side, angle and diagonal. For the edge, we discuss the relationship characteristics between adjacent edge and opposite edge from two aspects: position and size. For the angle, the adjacent angle and diagonal angle are the main aspects, and the relationship between size or concrete degree is discussed. For diagonal lines, the relationship between the position and size of the two diagonal lines and their relationship with edges and angles are discussed. In addition to the three main research angles of edge, angle and diagonal, it also involves area calculation, symmetry characteristics and so on. These are not only applicable to general parallelograms, but also to special parallelograms such as rectangles, diamonds and squares, and also to other quadrangles such as trapezoid. Therefore, students can learn from the above differences in their future studies. As a senior math teacher, Mr. Liu has been engaged in one-on-one junior high school math tutoring in Zhikang, and has coached a large number of senior high school entrance examination students, and achieved excellent results in the senior high school entrance examination. Teacher Liu teaches in the most acceptable way for students.