Final answer:
Given the slopes of quadrilateral DEFG, with two opposite sides having the same slope and the other sides having different slopes, it can be described as an isosceles trapezoid.
Step-by-step explanation:
The slopes given for the sides of quadrilateral DEFG are 14, -35, 14, and 12. We can determine the shape of this quadrilateral by analyzing the slopes of its sides. Since two opposite sides have the same slope (14), they are parallel to each other. The other two sides do not have the same slopes, but they are neither perpendicular (since the product of their slopes is not -1) nor parallel (as they do not have the same slope).
Generally, for a quadrilateral to be a parallelogram, both pairs of opposite sides must be parallel. Since only one pair of opposite sides here is parallel, quadrilateral DEFG is not a parallelogram but rather a trapezoid, specifically an isosceles trapezoid because the non-parallel sides do not have the same or a negative reciprocal of the slope of the parallel sides, implying they are not perpendicular.