For each of these the prompt is, “find as many missing things as you can.” And what I like about them is that it gave my students to use congruent triangles alongside other sorts of deductive moves. We have ways of finding missing angles in a diagram, we have other ways of finding missing lengths. A congruent triangle argument is just like that — it’s another way of using what you know to know a little bit more.
The other nice thing is that in each of these diagrams, there is information that we can’t know. I think it was good for my students to experience that too.
For each of these my routine was to show the image, state the prompt, ask for a raised thumb when you figured something out, assign partners, task them with finding more things out, quickly listing some of the lower-hanging fruit on the board, then discussing whatever I found most interesting in each diagram.
I thought it might be nice to make a set of practice problems to follow-up on these, but I haven’t gotten around to it yet.