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在平面几何的教学中经常会遇到与线段比有关的问题,本文试图通过一个平几问题来具体谈谈这类问题的一般解法并给出其拓展.(1)问题的提出:如图,在平行四边形ABCD的边AD上取点F,使得AF=1nAD,点K是直线AC与BF的交点,求证:AK=n1+1AC.证如图(1),设AK=λAC,由于四边形ABCD为平行四边?
In the teaching of plane geometry, we often encounter problems related to the line segment ratio. This article attempts to discuss the general solution to this type of problem through a series of problems and give an extension. (1) The problem is presented as follows: Take the point F on the side AD of the parallelogram ABCD so that AF = 1nAD, point K is the intersection of the straight line AC and BF, verify: AK = n1 + 1AC. As shown in Figure (1), set AK = λAC, due to the quadrilateral ABCD Is it parallel to the four sides?