The neutral line EF= 1/2(AB+DC)=h=2EG=2FH.

EG⊥AB in g, FH ⊥ ab in h = > quadrilateral EGHF is a rectangle = >; EF=GH=h

△AEG rotation after △ 180 degrees, g 'e = ge = & gtge+g 'e = h.

Delta △BFH rotation after delta 180 degrees, h 'f = FH =>h 'f+FH = H.

BC+AG+HB=2EF-GH=GH=h

So GH=HF+FH'=BC+AG'+CH'=GE+EG'=h,

After rotation, all four sides are equal, and all four internal angles are 90 degrees, which is a square.