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在解一元一次方程时,为了得到方程的解,我们常常需要对方程进行变形,使方程最终化为x=a的形式,从而求出方程的解.你还记得对方程变形的依据吗?那其实就是等式的性质.在证明两个三角形全等的过程中,为了证明两条线段或两个角相等,有时也需要用到等式的性质.下面举例说明.一、说明线段的和差相等例1(2011年.东莞)如图1所示,E、F在AC上,AD∥CB且AD=CB,∠D=∠B.求证:AE=CF.分析:注意到AE=AF+EF,CF=CE+EF,要证AE=CF,只需证AF=CE即可.这可通过证明AF所在的△ADF与CE所在的△CBE全等来实现.
When solving a one-time equation, in order to get the solution of the equation, we often need to deform the equation so that the equation is eventually transformed into the form of x = a to find the solution to the equation. Do you still remember the basis for the deformation of the equation? In fact, is the nature of the equation in the process of proof of equality of the two triangles, in order to prove that two lines or two angles equal, and sometimes also need to use the nature of the equation below to illustrate. Equivalent Example 1 (Dongguan, 2011) As shown in Figure 1, E, F are on AC, AD∥ CB and AD = CB, ∠ D = ∠ B. Confirmation: AE = CF Analysis: It is noted that AE = AF + EF, CF = CE + EF, to prove AE = CF, only need to prove that AF = CE can be achieved by demonstrating the △ ADF where AF is located and the CB where CBE congruent.