What are the minimum number of measurements required construct a unique parallelogram?
3
Since the opposite sides of a parallelogram are equal to each other, even if we know one side we need to know the measurement of its adjacent side. So, we have to know 2 measurements.
Now to construct the parallelogram, suppose that we have drawn one side. To draw another side, we need to know at least one angle.
So, in total, we need at least 3 measurements to construct a parallelogram.