Question

Quadrilateral EFGH is on a coordinate plane. Which statement is true?

Answer 1

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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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.)