As shown in the figure, in trapezoidal AB, CD and AD are parallel to BC, and square ABGE and square DCHF are bounded by two waists AB and CD respectively. Let the vertical line L of line segment AD intersect with line segment EF at point M, and intersect with line segment AD at point I ... Verify that point M is the midpoint of EF. (ABCD is not necessarily an isosceles trapezoid)

The picture below is my idea. It's not that hard. Take a look: Please divide a rectangle with a length of 5CM and a width of 1CM into five equal areas and make it into a square. In fact, it is four right triangles divided into 1× 1 squares and 1 × 2. A square is a chord graph.