??? Angle Angle Angle Postulate (AAA)

Drag the red points in the top half of the drawing to adjust the givens, then adjust the points to try to make congruent or non-congruent triangles in the bottom half.
Does Angle Angle Angle Postulate Exist?
Even though you can change the angles, and it appears the triangles stay congruent, what happens if you change the triangles? Do the angles stay congruent? Do the triangles stay congruent?[br][br]Angle Angle Angle Postulate DOES NOT EXIST!
– Scott Byerly, Chip Rollinson

Information: ??? Angle Angle Angle Postulate (AAA)