The first question, AE=AF, AE is perpendicular to DF. Firstly, it is proved that all triangles ADE are equal to triangle DCF. AE vertical DF can be obtained from congruent triangles property, AE=DF, angle DAE= angle CDF, and then the complementary angles of equal angles are equal.
Solution: (1)AE=DF, AE is perpendicular to DF, reason: quadrilateral ABCD is square, so AD=DC, angle ADC= angle C=90 degrees, because DE=CF, so triangle ADE is all equal to triangle DCF, because AE=DF, angle DAE= angle CDF, see here for detailed answers/exercises/mathematics/.
(1) As shown in figure 1, when point E moves from point D to point C and point F moves from point B, the connecting line AE and DF intersect at point P. Please write down the positional relationship between AE and DF and explain the reasons.
(2) As shown in Figure 2, when E and F move to the extension lines of DC and CB respectively, does the conclusion that AE and d F are connected in 1 still hold? Please answer "Yes" or "No" directly without proof.