I think you&#x27;re saying something a little too strong. I think such a measurement does provide <i>some</i> information about the dimensions of the quadrilateral being measured. I think it would be possible with a bounded number of observations to measure the lengths purely by measuring the angles. You would have to shift your perspective each time, but it shouldn&#x27;t take too many. So, each such measurement must contribute a non-zero amount of information about the dimensions.<p>Either that, or i&#x27;m misinterpreting your first sentence.