cant we prove “If the diagonals of a quadrilateral bisect each other, then it is a parallelogram” by showing that AD=BC and AB =CD???

Hi!

Yes, you can prove “If the diagonals AC and BD of a quadrilateral ABCD bisect each other at point O, then ABCD is a parallelogram” by showing AD = BC and AB = CD.

For this you firstly need to prove ΔAOD ≅ ΔCOB and ΔAOB ≅ ΔCOD.

Best wishes!