Which criteria must be true to conclude that ABCD is a parallelogram?

AE⎯⎯⎯⎯⎯≅EC⎯⎯⎯⎯⎯ and DE⎯⎯⎯⎯⎯≅EB⎯⎯⎯⎯⎯

AE=12BC

AC⎯⎯⎯⎯⎯≅BD⎯⎯⎯⎯⎯

AE⎯⎯⎯⎯⎯≅BE⎯⎯⎯⎯⎯ and DE⎯⎯⎯⎯⎯≅CE⎯⎯⎯⎯⎯
Parallelogram A B C D with diagonals A C and B D intersecting at E.