E, f, g and h are the midpoint of CD, AC, ao and od respectively.

Making auxiliary lines AD, OC

From the midline theorem, we know that GF = He and Hg = EF.

It is easy to prove that a congruent triangles ABD=CBO.

So AD=CO

That is, the midpoint line is a diamond.

The angle BCO=DAB=HGO is also obtained from the congruence formula.

Because the angle BCO+BOC = 90° and BOC = BGF.

So the angle HGF=HGB+BGF=90.

So it is a square.