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探究一题多解,不仅可以开阔同学们的解题思路,而且对于数学知识的灵活运用,融合贯通也很有帮助.我以勾股定理当中的一道典型例题为例,给同学们提供多种证法,希望对你们有所启发.图1例题如图1,在△ABC中,∠BAC=90°,AB=AC,P为BC上一点,求证:PB2+PC2=2PA2.分析由求证的式子自然地联想到勾股定理,但相关三线段并不在同一个直角三角形中,因此它指明了添加辅助线的方向——添加的辅助线与相关的线段组
To explore a multi-solution, not only can broaden the students’ problem-solving ideas, but also for the flexible use of mathematical knowledge, integration is also very helpful.I use the Pythagorean Theorem among a typical example, to provide students with a variety of Card law, I hope for your inspiration .Figure 1Examples as shown in Figure 1, in △ ABC, ∠ BAC = 90 °, AB = AC, P BC point, verify: PB2 + PC2 = 2PA2. The formula naturally remembers the Pythagorean theorem, but the relevant three-line segments are not in the same right-angled triangle, so it specifies the direction in which the auxiliary line is added - the auxiliary line added and the associated line segment