Thinking About Geometry Proofs - Do They Get It?

Another year and another chance to teach students about Geometric Proofs...however, they are all starting to seem the same to me - how can the students not see another another set of vertical angles - another line that is shared by two triangles - JUST WRITE DOWN REFLEXIVE ALREADY!

I often wonder if the students really understand what we are doing here - or are the students that are successful at proofs the ones that are super good at copying what I am doing?  Do students honestly  understand that SSA can't be used to prove triangles congruent, or do they think that I just don't want them to use those combination of letters because they spell a bad word if you look at it backwards???

No matter that I have explained until I am blue in the face...

I have honors students, so I think they should be able to understand, but do they...

I think that when I show students later in the year a "proof" of the Pythagorean Theorem - note: no two columns involved...that they appreciate a teenie tiny bit of the beauty of mathematics.

But, back to these congruent triangle proofs...I am open to suggestions on making them more exciting and fun - do you have any suggestions??

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