I think Jessica B's answer is spot-on (and it relates with me strongly with respect to my research in geometry), but I would like to add something in that direction, which I get from Anne Parreau who was teaching math to future primary schools teachers.
There is no such thing as an exact drawing.
There are precise drawing, there are enlightening drawings, there are beautiful drawings, but all of them cheat. They cheat a lot more than one expects before doing the following experiment.
Ask your student to draw a triangle with sides 3, 5 and 8 and observe. There should be three categories: those who say that it is not possible because two circles won't meet; those who will draw a very flat, but non-degenerate triangle, and those who will draw a flat triangle by cheating (i.e. not using fairly the rule and compass, but using their geometric knowledge to know what they should see, and then adapting there drawing to fit that knowledge). If you get even a single student who draws a fair (inexact) picture and says that it is not what should appear and ask for help, then you should congratulate him a lot.
Another one (again mentioned to me by Parreau): have your student draw a triangle with sides 3, 4 and 6, say, and then have them measure the angles and compute the sum. You should observe that many of them will change their measurement a posteriori to fit what they know, that the sum should be 180°. If you get some that discuss imprecisions or even just wonder why this is happening, you are blessed.
Let me finally add a personal touch. The previous example could be done with a triangle formed on the surface of earth by three cities, on a globe, realized by strings. You would need as large a globe as you can get to choose a not too large triangle, so that the sum of angles is definitely not 180° but not too far. Then you have some ground to discuss the assumptions of geometry and mathematical theorems in general, the questions of precisions, and why we want proofs rather than only measurement.