折叠问题的实质是对称问题,折痕是对称两点连线的垂直平分线,在解决这种问题时常用到直角三角形的相似、全等三角形、勾股定理等内容,以及方程、化归等数学思想.例1如图1,矩形ABCD的长AD=9cm,宽AB=3cm,将其折叠,使点D与点B重合,求对折后DE的长与折痕EF的长.分析当将长方形折叠, The essence of the folding problem is the symmetry problem. The crease is the vertical bisector of the symmetric two-point line. In solving this problem, the similarity, the equal triangle, the Pythagorean theorem, etc. of the right-angled triangle are often used, as well as equations, transformations, etc. Mathematical thinking. Example 1 In Figure 1, the length of the rectangle ABCD is AD = 9cm, and the width is AB = 3cm. Fold it so that the point D coincides with the point B. Find the length of the folded back DE and the length of the fold EF. Rectangular folding,