《数学通报》2006年第4期上刊登的1601号问题是:凸四边形两对角线的平方和等于四条边的平方和,求证:此四边形是平行四边形.问题提供人给出的解答过程较为繁复,且技巧性强,不易掌握.笔者提供一种较为简捷的向量证法,供读者参考.证(如图)由题意AC2+BD2=AB2+BC2+CD2+DA2,因为AC=AB The issue of No. 1601 published in No. 4 issue of Mathematical Bulletin, 2006 is: The sum of the squares of the two diagonals of a convex quadrilateral is equal to the sum of the squares of the four sides. Proof: The quadrilateral is a parallelogram. The problem is given by the questioner. Complex, and skillful, not easy to grasp. The author provides a relatively simple vector proof method, for readers reference. Certificate (pictured) by the title AC + BD2 = AB2 + BC2 + CD2 + DA2, because AC = AB