This topic mainly examines the nature of the square, congruent triangles's judgment and similar triangles's judgment and nature. It is the key to solve the problem by skillfully using the properties of the square to find the relationship between the corresponding angle and the corresponding edge.

The first question, according to the meaning of the question, obtains the S quadrilateral abfe = 4-1/2ed * df-1/2bc * fc, and then obtains the answer.

Solution: (1) Since PE is perpendicular to AD and PF is perpendicular to DC, the quadrilateral EPFD is rectangular with AP = X. See this/Exercise/Mathematics /800057 for detailed answers and ideas, as shown in Figure 1 and 2. It is known that the quadrilateral ABCD is a square, and there is a moving point P on the ray AC, which is PE⊥AD (.

(1) In figure 1, let the side length of square ABCD be 2, the area of quadrilateral ABFE be y, and AP=x, and find the functional expression of y about x;

(2) Conclusion: GB⊥EF is valid for both figure 1 and figure 2. Please choose any number to prove it.

(3) Please prove according to Figure 2: △ FGC ∽△ PFB.

Come on, I wish you progress in your study!