Question

ABCD is a square. Given only the choices below, which properties would you use to prove AEB ≅ DEC by SAS? The diagonals are ⊥ to each other. Opposite sides are | |. The diagonals bisect each other. All sides are congruent.

Answer 1

All sides of a square re equal and opposite sides are parallel to each other. 
Assuming that E is the point where the diagonals intersect (since we are not told in the question), then AEB ≅ DEC.
 By SAS, 
  2 sides are equal. That is AE = EC and DE = EB.
  The triangles share a common angle. That is <DEC=<AEB

The property used the diagonals bisect each other.