The four moving points P.Q.E.F start from the vertex A.B.C.D of the square ABCD and move along AB at the same time. BC.CD.DA to B.C.D.A at the same speed.

Available AP=BQ=CE=DF

PB=QC=ED=FA

You can get △ APF △ BQP △ CEQ △ DFE.

PQ=QE=EF=FP。

∠FPA=∠PQB

∠PQB+∠QPB=90。

So ∠FPA+∠QPB=90.

∠FPQ=90

So PQEF is square.

2.PE always crosses the intersection of diagonal AC and BD (geometric center of square ABCD)

3. It is the largest when it coincides with A, B, C and D, and the smallest at the midpoint of each side of a square A, B, C and D..

The largest is the area of square ABCD, that is, the square of side length,

The smallest is the largest half.