For coordinate goemetry, what do you have to prove to say that a rhombus is a rhombus?

So far, I have proving all sides are congruent, and proving that the diagonals are not congruent because by definition, a rhombus does not have congruent diagonals and has congruent sides. I have one more, I don't know if it's necessary, but to prove that diagonals are perpendicular? How about proving angles are NOT right angles?