To construct a parallelogram given its length of diagonals, which of the following additional information is required?
The angle between the diagonals
We know diagonals of a parallelogram bisect each other. As we are given the length of the diagonals, we can draw unique set of diagoanls if the angle between them are given.
Therefore, if we know ∠AOD we can construct the diagonals and join the 4 end points to form a paralellogram.