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勾股线段问题,即满足a2+b2=c2关系的三条线段的证明或计算问题,知识点多,内容丰富,趣味性强,解题的方法灵活,既有几何变换的手法,又可通过代数运算的途径解答.这对于培养思维的发散能力和创新意识十分有利.以下几例,条件和结论中的边、角类元素间的关系松散, 利用旋转变换的方法,使分散的条件集中,两者间的关系便显露出来了: 均与直角三角形中的勾股定理有关. 旋转变换有一个直观又有价值的性质,即旋转对象各元素(角、线段
The problem of the line segment of the gouache segment, that is, the problem of proof or calculation of the three line segments satisfying the relationship of a2+b2=c2, is rich in knowledge, rich in content, and interesting, flexible in solving problems, and has both geometric transformation methods and algebra. The solution to the operation. This is very beneficial for cultivating the divergence and innovation consciousness of the thinking. In the following cases, the relationship between the edge and corner elements in the conditions and conclusions is loose, and the method of rotation transformation is used to concentrate the scattered conditions. The relationship between the two is revealed: Both are related to the Pythagorean Theorem in a right-angled triangle. The rotation transformation has an intuitive and valuable property that is to rotate the elements of the object (corners, line segments).