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在《四边形》这一章节的新课讲授中,我们通过一个例题,探究性地学习了三角形中位线的性质定理;随着学习的不断深入,在本章节的拓广探究中,我们进一步研究了梯形中位线的性质定理。我们的认知过程,总是符合一定的学习规律,由浅入深,一步一步逐渐深入。并且,我们还发现事物的内在联系:在横向的对比中,我们建立了两者的联系,将三角形推广到四边形;在纵向的对比中,三角形中位线的上下移动,得到两个三角形,新的三角形与原三角形的对应边的比相等(见《相似形》),那么,梯形是否也存在着类似于三角形的边关系呢?“梯形中位线的推广”由此展开。
In the lecture of the new course in the chapter “Quadrilateral”, we have probed into the nature theorem of bit lines in triangles through an example. With the continuous deepening of study, we further extend the study in this chapter The property theorem of the bit line in trapezoid is studied. Our cognitive process, always in line with certain laws of learning, from shallow to deep, step by step in-depth. And we also find that the internal relations of things: in the horizontal contrast, we establish the relationship between the two, the triangle extended to the quadrilateral; in longitudinal contrast, the triangle in the vertical line up and down to get two triangles, the new Triangle and the corresponding side of the original triangle equal ratio (see “similar shape”), then the trapezoidal triangle-like edge also exists there? “Trapezoidal bit line extension ” thus expand.