in a quadrilateral ABCD, AB=BC & CD=DA then the quadrilateral is a

Let ABCD be the quadrilateral in which diagonals AC and BD bisects each other.

Given that AB = BC and CD = DA.

According to the above conditions,  ABCD is a rhombus because if the diagonals of a quadrilateral bisect each other, then it is a parallelogram and opposite sides of a parallelogram are equal.