I’m not teaching geometry this year, but one of the biggest hurdles the kids had to overcome was that they’re expected to have some facility with recognizing midpoints, angles and so on, but that they’re not allowed to assume that what they see actually is that way unless it’s labelled as such.
Matthias Wendel has made an eyeballing game where he gives you geometric constructions that are a bit off, and you try to fix them. I do a little bit better than average, but two things become clear very quickly:
1) You can improve your guessing ability through practice.
2) No matter how good you get, you still won’t be able to tell perfectly every time.
This solves a duel purpose – it explains, viscerally, that what you think you see is not always actually what you think it is, and secondarily it shows why, even if you don’t get it perfect, you need to be able to show congruency or angle measure in order to make a mathematical argument.
An added bonus in the process is that you get a good understanding of some basic geometry principals. My guess is that’s it’s probably worth about a half hour of computer lab time, with perhaps some reflection thrown in to round out the period.