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课本上的习题,大多数是经过严格筛选的.内涵丰富,在培养学生能力方面有着不寻常的作用,尤其被限制了证法的刁题.除具有一般习题的功能.还具有特殊效应.因此,在充分发掘习题的潜在功能的同时,要深刻理解限制习题证法的意图.下面,仅就《几何》第二册39页11题谈谈这个问题. 题:设AD、BE和CF是△ABC的三条高.求证:AD·BC=BE·CA=CF·AB(用比例线段证明). (分△ABC是锐角三角形、直角三角形和钝角三角形三种情况)
Most of the exercises in textbooks are rigorously screened. They are rich in content and have an unusual effect in cultivating student abilities. In particular, they have limited the issue of phrasing. Apart from the functions of general exercises, they also have special effects. While fully exploring the potential functions of exercises, it is necessary to profoundly understand the intention of restricting the exercise of the exercises. In the following, this issue will only be discussed on the basis of “Geometry” in Book 2 and page 39. Question: Let AD, BE, and CF be △ ABC’s three high. Proof: AD · BC = BE · CA = CF · AB (Prove with Proportional Segments). (△ △ ABC is an acute triangle, right triangle and obtuse triangle three cases)