triangle EOD is rectangular => the median from O : OG = ED/2 = EO => EOG is equilateral and the ungle DEO is 60 degrees => ungle AEO is 120 degrees, and being isoscel => the ungle EAO = 30 degrees.
In triangle GOD we have : ungle GOD is 30 degrees, being isoscel => ungle GDO is 30 degrees too => ungle GDO = ungle EAO => triangle ADO is isoscel and AO=OD => the diagonals AC = BD .
In a paralellogram, if the diagonals are equal => rectangle. So it is.
I hope u understood the explanation,as i didnt find any better method to write...