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Answer:
a. AC ≅ BD
Explanation:
All four sides are marked as being the same length. This means the figure is a parallelogram and a rhombus.
Diagonals bisect each other in any parallelogram. They are perpendicular, and bisect the corner angles, in any rhombus. Choices b, c, and d add no new information.
In order to show the figure is a square, you must show this rhombus is a rectangle: the diagonals must be the same length. That is you must show ...
AC ≅ BD
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Additional comment
You may be given problems with coordinates, and asked to show the figure is a parallelogram, rectangle, rhombus, or square. Often, the problem is given with the intent that you use slope and length formulas on the given points to prove opposite sides are parallel and the same length. IMO, these problems are much simpler if you show the appropriate relation exists between the midpoints, slopes, and lengths of the diagonals.