平面几何中有关正方形的证明题,证明时往往要充分运用它的角都是直角和各边相等的性质,同时要注意到它的对角线的所有性质——相等、互相平分、互相垂直及平分一组对角,有时还要用到它的边长与对角线长的比或对角线长的一半与边长的比都是1:2~(1/2)的性质.这样,才能顺利地探索出这类问题的证法. In the proof of squares in plane geometry, it is often necessary to make full use of the fact that the angles of the squares are all equal to the right angles and the sides. At the same time, we must pay attention to all the properties of the diagonals—equal, mutually even, and perpendicular to each other. Dividing a set of diagonals, sometimes using the ratio of the length of its sides to the length of its diagonal lines or the ratio of the length of half of the diagonal lines to the length of its sides, is 1:2~(1/2). Thus, Can successfully explore the proof of this type of problem.