Proof: By Euclid
(related to Corollary: Parallelogram  Defining Property II)
This follows immediately from Prop 1.34 and the definition of a parallelogram or a rhombus.
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References
Adapted from CC BYSA 3.0 Sources:
 Callahan, Daniel: "Euclidâ€™s 'Elements' Redux" 2014
Adapted from (Public Domain)
 Casey, John: "The First Six Books of the Elements of Euclid"