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平面几何的证明问题中,有一类题目是关于线段的和差问题即证明两条线段的和(差)等于另一条线段.在证明过程中,一般需要添加辅助线,而最常见的添加方法为延长法(补短)或截取法(截长).若要证的线段和差形如线段a=b+c.延长法(补短):根据图形,适当作出线段d=b+c,然后证:d=a;截取法(截长):根据图形,适当作出线段e=a-b,然后证:e=c.
One of the problems with proofs of plane geometry is that of the sum-of-difference problem for line segments, which proves that the sum (difference) of the two line segments equals the other line segment. In the proof process, it is generally necessary to add guidelines, and the most common addition is Extension of the law (make up short) or interception method (cut). To the card line and the difference line segment a = b + c. Extension method (complement short): According to the graph, the appropriate segment d = b + c, Card: d = a; interception method (cut): According to the graphics, the appropriate section e = ab, and then card: e = c.