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对于某些几何题来说,常可立足于三角形的一条高,进而构造(或证明)第二条高找出垂心,再巧妙应用垂心的性质来解题往往十分简捷明快,可起到事半功倍的效果或使证法新颖独特,别具一格。然而利用垂心解题一般刊物谈及甚少,下面就如下问题举例说明。一、证明两线垂直例1 已知如图,Rt△ABC的直角边AB为一边向形外作正方形ABDE,延长AB至F,使BF=AC,CD与AB交于H,
For some geometric questions, it is often possible to base a height on the triangle, and then construct (or prove) the second height to find out the vertical center of mind, and then apply the nature of verticality to solve the problem is very simple and straightforward, can play a multiplier role. The effect can be unique and novel, unique. However, there is very little talk about using the general publication of problem solving. Below is an example of the following issues. I. Prove that the two-line vertical example 1 is known. As shown in the figure, the right-angled edge AB of Rt △ ABC is a square-shaped ABDE, extending AB to F so that BF=AC, CD, and AB intersect at H.