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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 BY-SA 3.0 Sources:

1. Callahan, Daniel: "Euclid’s 'Elements' Redux" 2014

Adapted from (Public Domain)

1. Casey, John: "The First Six Books of the Elements of Euclid"