If you had some sort of dot system in the background to indicate grid points for the bisecting, the line players draw could snap to that, if the shapes are then aligned to that grid the chance of player/game detection error would go away. Some indication of a mistake would be good sound wise. Also the repetiviness of it could be helped with perhaps having to make multiple cuts in order to create symmetry. I think progression would be better shaped around more complex shapes to do over time with multiple cuts.
Great work!