Diagonals of a Parallelogram

Side lengths of diagonals are given.[br]Congruent angles are color coded.
Why do you think you can move vertices A, B and C but not D?[br]Are there any congruent triangles? How do you know?[br]Without their values being known, how do you know that certain angles are congruent?

Information: Diagonals of a Parallelogram