The problem of moving angles is a difficult problem in the first semester of the seventh grade in junior high school, and it is a headache for most students. The main contents of the investigation include: the definition of angles, the definition of angle bisector, the ratio of angles, the unary equation, the expression and calculation of angles, the ideas of classification and discussion, etc., which almost cover most of the knowledge points in the first semester of the first semester of junior high school, and the investigation is relatively flexible. Due to the lack of depth in the class, there is often only one question in a set of comprehensive practice questions, and the amount of questions is not enough. Solution: First, have a firm grasp of the basics, especially the geometric language of the angular bisector; secondly, master the idea of problem solving, train the idea of classification and discussion, the idea of combining numbers and shapes, etc.; Finally, practice makes perfect, and a lot of practice to strengthen your thinking of doing problems. The moving angle problem is a knowledge point that tests students' mathematical thinking and problem-solving ability. In order to better grasp the problem of moving angle, we need to start from the following aspects:
First of all, it is necessary to understand the concept of angle in depth. An angle is a measure that describes the magnitude of the angle between two rays or line segments, and its unit is degrees (°) or radians. When solving the problem of moving angle, we need to pay attention to the change of angle and how to use the angle operation to solve the problem.
Second, grasp the definition and nature of the angular bisector. An angle bisector is a line segment that divides an angle into two equal small angles, and it has some important properties, such as equal distances from the point to both sides of the angle on the angle bisector. Understanding these properties can help us solve some of the moving angle problems associated with angular bisectors.
In addition, we need to understand the ratio of angles. The ratio of angles refers to the proportional relationship between two angles, and is usually used to describe the change in the speed or direction of rotation of two angles. Solving problems related to angular ratios requires us to apply the arithmetic of proportions and geometry.
The unary equation is also an important tool for solving the problem of angle of motion. When dealing with problems related to angle changes, we often need to solve for unknowns by setting up equations. Mastering the solution of a one-dimensional equation allows us to quickly find a way to solve the problem.
When solving the problem of moving angles, we also need to pay attention to the expression and calculation of angles. There are many ways to express angles, such as degrees, radians, trigonometric functions, etc., and choosing the right way to calculate can simplify the problem. In addition, categorical discussion ideas are also the key to solving the problem of moving angles. For some complex questions, we need to classify and discuss according to different situations in order to consider the problem comprehensively and arrive at the correct answer.
In summary, solving the problem of moving angles requires us to comprehensively apply the basic knowledge of mathematics, including the concept of angles, the properties of angle bisectors, the ratio of angles, the unary equations, and the expression and calculation of angles. By understanding this knowledge in depth and mastering the ideas and skills to solve problems, we can gradually improve our ability to solve moving angle problems.
The following summarizes the common formulas in such questions, collects 6 types of questions for you, grasps the knowledge points and insists on practicing, I hope it will be helpful to you, learn it quickly.