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1问题的提出我们知道:正方形四边形ABCD中,点Z、L、M、W分别在AB、BC、CD、DA的延长线上,AB=BZ,BC=CL,CD=DM,DA=AW.则四边形ZLMW是正方形.本文给出几个生成正方形的有趣结论。2来自正方形的挑战命题1:如图2,四边形ABCD中,点Z、L、M、W分别在AB、BC、CD、DA的延长线上,AB=BZ,BC=CL,CD=DM,DA=AW.若四边形ZLMW是正方形,则四边形ABCD是正方形。这个问题困惑了我很长时间,最近有了灵感,先证明一个引理.
1 PROBLEM PROBLEM We know that the points Z, L, M and W in the square quadrilaterals ABCD are on the extension lines of AB, BC, CD and DA respectively. AB = BZ, BC = CL, CD = DM and DA = AW. Then the quadrilateral ZLMW is a square.This article gives several interesting conclusions for generating a square. 2 Challenges from Squares Proposition 1: As shown in Figure 2, quadrilateral ABCD points Z, L, M and W are on the extension of AB, BC, CD and DA respectively. AB = BZ, BC = CL and CD = DA = AW. If the quadrilateral ZLMW is a square, the quadrilateral ABCD is a square. This question puzzled me for a long time, recently inspired, first to prove a lemma.