18 points
quadrilateral abcd has coordinates a (3, −5), b (5, −2), c (10, −4), d (8, −7). quadrilateral abcd is a rectangle, because opposite sides are congruent and adjacent sides are perpendicular
square, because all four sides are congruent and adjacent sides are perpendicular
parallelogram, because opposite sides are congruent and adjacent sides are not perpendicular
rhombus, because all four sides are congruent and adjacent sides are not perpendicular

The answer is (c) parallelogram, because opposite sides are congruent and adjacent sides are not perpendicular.

Step-by-step explanation: The co-ordinates of the vertices of quadrilateral ABCD are given to be A(3,-5), B(5,-2), C(10,-4) and D(8,-7).

The lengths of the sides are as follows -

Therefore, AB = CD  and  BC = DA.

Also, the slopes of the sides AB(m), BC(n), CD(o) and DA(p) are as follows

For two lines to be perpendicular, the product of their slopes should be -1 and for them to be parallel, their slopes must be equal. So, here no two pair of lines are perpendicular. But, m = o and n = p and so, the opposite sides are parallel.   

Since the opposite sides are congruent and parallel, but not perpendicular, so the quadrilateral ABCD is a parallelogram.

Thus, the correct option is (c).

Parallelogram, because opposite sides are congruent and adjacent sides are not perpendicular

Step-by-step explanation:

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