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The slopes of the sides of quadrilateral defg are 14, -35, 14, and 12. Which statement correctly describes the shape of quadrilateral defg?

1) Quadrilateral defg is a parallelogram because there are two pairs of equal slopes, and thus two pairs of parallel sides.
2) Quadrilateral defg is a trapezoid because there is one pair of equal slopes, and thus one pair of parallel sides.
3) Quadrilateral defg is not a trapezoid because there are no pairs of parallel sides.
4) Quadrilateral defg is not a parallelogram because there are no pairs of parallel sides.

1 Answer

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Quadrilateral DEFG, with two pairs of equal slopes, is a parallelogram because these slopes imply two pairs of parallel sides.

The question involves understanding the properties of quadrilaterals and how the slopes of their sides can determine their shape. Given that quadrilateral DEFG has sides with slopes of 14, -35, 14, and 12, we look for pairs of equal slopes to determine parallel sides. Since there are two pairs of equal slopes (14 and 14), this indicates that two pairs of opposite sides are parallel.

According to the properties of quadrilaterals, this makes quadrilateral DEFG a parallelogram. Therefore, the correct statement to describe the shape of quadrilateral DEFG is that it is a parallelogram, which aligns with option 1) Quadrilateral defg is a parallelogram because there are two pairs of equal slopes, and thus two pairs of parallel sides.

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