Answer:
see below
Step-by-step explanation:
Opposite sides are parallel in a parallelogram, so if they have different slope, the figure will not be a parallelogram.
_____
Comments on other answer choices
If the slope of diagonal EG is perpendicular to that of diagonal FH, it only proves the figure is some sort of kite. The figure may or may not be a parallelogram.
Adjacent sides being different lengths does not prove anything (except that the figure is not a rhombus).
Proving angle F is a right angle does not prove anything else about the shape of the figure. The figure may or may not be a parallelogram. (If it is a parallelogram, it is also a rectangle.)
