Students are frequently confused by us harping on the importance of things that seem obvious: because we hardly ever show them the cases where the theorems are false.
But think of the infinite number of line that are not parallel!! Lets spend some time exploring all those wrong cases... and see what goes wrong... then we can truly appreciate the special case of parallel lines.
The Congruent Game at the end I feel can get some kids to pay some attention to how precise it must be. The scoring is arbitrary: floor(-2000 + 2000 (1.2^(1 / (180 - difference in angles))) I think it is possible for it to report back "infinity". Good luck getting it!
