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.
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<em>Comments on other answer choices</em>
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.)
