When do you choose to prove this? Do you begin intuitively and then only prove when students have knowledge of angles in parallel lines? Could you use the proof in cell 1 immediately?

How do you choose to prove that the angles in a triangle sum to 180 degrees? One of the techniques above, all of them?

Could you utilise the idea of goal free problems so that students identify all angles they can in the 4 cases above and then you reveal that they have just proven that the angles in a triangle add to 180 degrees in 4 ways?

To have students complete a proof, I developed one that provides multiple avenues in the final step, so as to increase the chances of a proof from more students: