|In any parallelogram the complements of the parallelograms about the diameter equal one another.|
|Let ABCD be a parallelogram, and AC its diameter, and about AC let EH and FG be parallelograms, and BK and KD the so-called complements.
I say that the complement BK equals the complement KD.
|Since ABCD is a parallelogram, and AC its diameter, therefore the triangle ABC equals the triangle ACD.||I.34|
|Again, since EH is a parallelogram, and AK is its diameter, therefore the triangle AEK equals the triangle AHK. For the same reason the triangle KFC also equals KGC.||I.34|
|Now, since the triangle AEK equals the triangle AHK, and KFC equals KGC, therefore the triangle AEK together with KGC equals the triangle AHK together with KFC.||C.N.2|
|And the whole triangle ABC also equals the whole ADC, therefore the remaining complement BK equals the remaining complement KD.||C.N.3|
|Therefore in any parallelogram the complements of the parallelograms about the diameter equal one another.|
Next proposition: I.44