3. parallelogram
step-by-step explanation:
we turn each of our sides into direction vectors
ab=b-a=(3 - 7, 1 - 0) = (-4, 1)
bc=c-b=(1,6)
cd=d-c=(4,-1)
da=a-d=(-1,-6)
we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram. we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2. so it's not a square or a rhombus.
we check the dot product of direction vectors of adjacent sides. we have
ab dot bc = -4(1) + 1(6) = 2
that's not zero so the sides are not perpendicular. we've ruled out rectangle.
the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.