we turn each of our sides into direction vectors
ab=b-a=(3 - 7, 1 - 0) = (-4, 1)
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.
could you provide figure.