Show and Tell: Resist the great temptation

The first example is a demonstration related to the sum of the angles. The second is from an article by a mathematician with the word "Lament" in it. Drag vertices around. What will STUDENTS see/notice/come to understand for themselves? It is (too) easy for (us) teachers to use dynamic geometry environments to show what WE know rather than as a tool to help students develop their own understanding.