For the given quadrilateral ABCD:

Length of AB = sqrt(8^2 + 1^2) = sqrt 65, slope of AB = (1/8)

Length of BC = sqrt(4^2 + 7^2) = sqrt 65, slope of BC = -7/4

Length of CD = sqrt(8^2 + 1^2) = sqrt 65, slope of CD = 1/8

Length of DA = sqrt(7^2 + 4^2) = sqrt 65, slope of DA = -7/4

So we have a quadrilateral with all sides equal and opposite sides parallel to each other. But the adjacent sides are not perpendicular to each other.

**The quadrilateral ABCD is a rhombus.**

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