论文部分内容阅读
证明ab+cd=ed型的线段关系式,一般地说,有两种思路: 一、分析法其要点是:通过分析,得出应如何添辅助线,从而找到证题的关键。二、代数法其要点是:找出题中的变量将欲证等式中的有关量化为变量的函数,从而使问题转化为证明代数或三角恒等式。下面通过例题来说明。例1 △ABC中,∠A的平分线交BC于D,求证 AD~2+BD·CD=AB·AC。证法一 (分析法) 分析欲使证式成立,显然AD~2应为AB·AC的一部分。因此,若能在AB上找到点X,使 AD~2=AX·AC,①
Prove that ab + cd = ed type of line relations, in general, there are two ideas: First, the main point of the analysis method is: through analysis, it is concluded how to add auxiliary line, so as to find the key to the test. Second, the main point of algebraic method is: find the variable in the question will want to prove the function in the equation quantified as a variable, so that the problem is transformed into a proof algebra or a trigonometric identity. The following examples illustrate. In case 1 △ABC, the bisector of ∠A was submitted to BC in D, and AD~2+BD·CD=AB·AC was confirmed. Proof One (Analysis) Analysis To make the proposition form, it is obvious that AD~2 should be part of AB•AC. Therefore, if you can find point X on AB, make AD~2=AX·AC,1