Answer:
a kite or a square
Explanation:
The fact that the diagonals are congruent is irrelevant, unless you also know something about where they cross each other.
A kite has perpendicular diagonals. If they happen to bisect each other, then the result is a rhombus. If the diagonals are congruent, then that rhombus is a square.
Other ways to get there
A pair of congruent diagonals that cross each other symmetrically will define a trapezoid. If they also bisect each other, the result is a rectangle. If the diagonals of that rectangle are perpendicular, then it is a square.