(1) You must master the basic knowledge firmly. Only on this basis can you talk about how to learn it well. For example, when we prove similarity, if we use the method that the two sides are proportional and the included angle is equal, we must pay attention to the angle we are looking for, not other angles. When answering the symmetry axis of a circle, you can't say its diameter, but the straight line where the diameter lies. Such details must be paid enough attention to and firmly grasped in peacetime. Only in this way can we learn geometry well.
(B) good at summing up, familiar with the common features of graphics. For example, as shown in the figure, given three * * * lines of A, B and C respectively, with AB and BC as edges, we can make equilateral △ABD and equilateral △BCE. If there are no other additional conditions, what conclusions can be found from this diagram?
If we can sum up through many exercises, in general, if there are two equilateral triangles with common vertices, a pair of rotating congruent triangles will inevitably appear, then we can easily draw △ Abe △ DBC. On the basis of this pair of congruent triangles, we will also draw △ EMB △ CNB, △MBN is an equilateral triangle, MN∨AC and so on. There are many such typical figures in geometry learning, so we should be good at summarizing them.
(3) Be familiar with the common focus of solving problems, and often use auxiliary lines to refine big problems into small ones, thus solving problems one by one.
When we have no practical solution to a problem, we should be good at grasping the focus that may help you solve the problem. For example, if a special angle appears in a non-right triangle, you should immediately think of constructing a right triangle vertically. Because special angles only work in special shapes. For another example, if a circle has a diameter, you should immediately think of connecting 90 circumferential angles. When we encounter the problem of trapezoidal calculation or proof, we must first know which auxiliary lines can be used when we encounter trapezoidal problems, and then analyze the specific problems. For example, what do you think of when the topic talks about the midpoint of the trapezoidal waist? You must think of the following points. First of all, you must think of the midline theorem of trapezoid. Second, you must think that you can translate one waist across the midpoint of the other. Third, you must think that you can connect a vertex with the midpoint of the waist and then extend it to form an congruent triangle. Only by memorizing these possible auxiliary lines can we solve the problem well. In fact, many times as long as we grasp these common points and work hard, the problem will be solved. In addition, as long as we think of it, we must be willing to try. Only when you do it can we succeed.
(4) Comprehensive consideration of problems is also very important for learning geometry well. In geometry learning, we often encounter problems that can be solved in two or more situations, so how can we solve these problems better? This depends on the usual bit by bit accumulation, and we should be familiar with the more common problems considered in different situations. For example, when it comes to the angle of an isosceles triangle, we should consider whether it is the top angle or the bottom angle; When it comes to the edge of an isosceles triangle, we should consider whether it is the bottom or the waist; When talking about the intersection of a straight line and a circle at a point, we should consider three positional relationships between the point and the circle, so we should draw three kinds of figures. This kind of situation is very common in geometry learning, so I won't list them one by one here, but we must pay attention to whether we should consider the situation when doing the problem. Many times, you usually focus on accumulation. I have this question in my heart, and I will naturally think of it when I do the problem.
In short, to learn geometry well, we must firmly grasp the basic knowledge, pay attention to the usual accumulation, be good at summing up and be familiar with the common points of solving problems. Of course, to do this, you must have a certain amount of practice. We don't advocate the tactics of asking questions, but it is necessary to do appropriate exercises. Only the accumulation of quantity can achieve a qualitative leap.