As shown in the figure, in ladder ABCD, AD / / BC, point E is on diagonal BC, and angle DCE = angle ADB, if 1. In the trapezoid ABCD, AD / / BC, point E is on the diagonal BC, and angle DCE = angle ADB. If BC = 9, CD: BD = 2:3, find the length of CE. 2. In the triangle ABC, ah is perpendicular to BC, h, CF is perpendicular to AB, f, D is a point on AB, ad = ah, de / / BC, prove: de = CF 3. After cutting a square from a rectangle, the remaining rectangle is similar to the original rectangle, and find the ratio of the short side to the long side of the original rectangle

As shown in the figure, in ladder ABCD, AD / / BC, point E is on diagonal BC, and angle DCE = angle ADB, if 1. In the trapezoid ABCD, AD / / BC, point E is on the diagonal BC, and angle DCE = angle ADB. If BC = 9, CD: BD = 2:3, find the length of CE. 2. In the triangle ABC, ah is perpendicular to BC, h, CF is perpendicular to AB, f, D is a point on AB, ad = ah, de / / BC, prove: de = CF 3. After cutting a square from a rectangle, the remaining rectangle is similar to the original rectangle, and find the ratio of the short side to the long side of the original rectangle

3. Let the short side of this rectangle be 2. From the meaning of the title, we can get: the long side is the root sign 5 and then minus 1. Therefore, this rectangle is a golden rectangle. The ratio of the short side to the long side is the root sign 5 and then minus 1 to 2