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化归思想(即化未知为已知)是一种重要的数学思想,在解数学题时经常用到.下面就一道常见的习题为例,说一说如何运用化归思想来培养我们的创新思维和解题能力.一、一题多解,活化思维例1如图1,AB//CD,EPF是AB、CD之间的一条折线,P是折点.试说明∠EPF=∠1+∠2.分析:“两条平行线被第三条直线所截”是平行线中的基本图形,要把图1变成基本图形,按我们所学的知识应将折线分段考虑,这样就有如图2～图5所示的四种方法.解法1:如图2,过点P作PG∥AB,则
To return to the idea (that is, the unknown is known) is an important mathematical thought, often used in solving mathematical problems. The following is a common exercise as an example, to talk about how to use the idea of fate to foster our innovation Thinking and problem-solving skills. One, one problem more solutions, activation thinking Example 1 As shown in Figure 1, AB / CD, EPF is AB, a line between the CD, P is the turning point.Please note ∠EPF = ∠1 + ∠ 2. Analysis: “Two parallel lines are cut by the third line ” is the basic graphics in parallel lines, to become the basic graphics in Figure 1, according to what we have learned should be considered broken lines, In this way, there are four methods as shown in Fig. 2 to Fig. 5. Solution 1: As shown in Fig. 2, P