In any parallelogram the complements of the parallelograms about the diameter are equal to one another.
Let ABCD be a parallelogram, and AC its diameter; and about AC let EH, FG be parallelograms, and BK, KD
the so-called complements; I say that the complement BK is equal to the complement KD. For, since ABCD is a parallelogram, and AC its diameter,
For the same reason
the triangle AEK together with KGC is equal to the triangle AHK together with KFC. [C.N. 2] And the whole triangle ABC is also equal to the whole ADC; therefore the complement BK which remains is equal to the
complement KD which remains. [C.N. 3] Therefore etc.
Q. E. D. 1 2