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1.六年制重点中学高中《解析几何》第一章第9节“两条直线的平行与垂直”中推证了两条有斜率的直线互相垂直的充要条件是:k_1=-1/k~·在证明其必要性时画了两个图(P_(39)): 这两个图是根据l_1、l_2的交点与x轴的相对位置来区分的:图甲中两直线交点在x轴上方,图乙中两直线交点在x轴下方.笔者认为,还应增加两直线的交点在x轴上的情形,这才比较完整。这三种情形得出α_1=α_2+90°的过程都略
1. In the sixth chapter “Analytic Geometry,” the first chapter of Chapter 9 “Analytic Geometry,” “Parallel and Vertical of Two Lines,” magnifies the necessary and sufficient conditions for two straight lines with slopes to be perpendicular to each other: k_1=-1/ k~· Draw two graphs (P_(39)) to prove its necessity: These two graphs are based on the relative positions of the intersection of l_1 and l_2 with the x axis: the intersection of two lines in graph A is in x Above the axis, the intersection of the two lines in Figure B is below the x-axis. I believe that we should also increase the intersection of the two straight lines on the x-axis, which is more complete. These three situations lead to the process of α_1=α_2+90°.