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观察分析图形,是几何教学的关键之一。然而,初学几何的学生往往一遇到复杂的图形就无从下手。有的虽然知道复杂图形是由一些简单图形构成的,但由于图中某些线条(包括辅助线)的连接、重合、交织,人脑很难将其中的简单图形清醒地分离出来,即很难做到只看图形的某一部分。为了解决这个问题,我们在教学中采取了“图形分离”的作法——将复杂图形中的简单图形分离出来分析,达到了化难为易的目的。例1 在图中,直线EF与AC被第三条直线所截,及AB、DF被第三条直线所截时,哪些角构成同位角、内错角、同旁内角? 分析:若所给图形是图2,学生可轻而易举地回答这个问题。但对于图1,就很少有人得出圆满的答案。现将图1分解成若干如图2的情形,移出观察。
Observing and analyzing graphics is one of the keys to geometry teaching. However, beginner geometry students are often unable to start with complex graphics. Some of them know that complex graphics consist of some simple graphics. However, due to the connection, overlap, and interweaving of certain lines (including auxiliary lines) in the diagram, it is difficult for the human brain to separate the simple graphics from it clearly. Do only look at some part of the graph. In order to solve this problem, we have adopted the “graphic separation” approach in teaching—the analysis of simple graphics in complex graphics has achieved the goal of making it difficult to change. Example 1 In the figure, when straight lines EF and AC are cut by the third straight line, and when AB and DF are cut by the third straight line, which corners form an azimuth angle, an inner angle error, and a side angle? Analysis: If given The graph is Figure 2. Students can answer this question easily. However, for Figure 1, few people have come to a satisfactory answer. Figure 1 is now broken down into a number of cases as in Figure 2, removed from the observation.