Sides qu and da of quadrilateral quad are parallel. sides ua and da each measure 4 inches. what additional information would guarantee that quadrilateral quad is a rhombus?

The additional information that will guarantee that the quadrilateral QUAD is a rhombus would be that all the sides have equal length, and that the opposite angles are the same.

The rhombus is a simple quadrilateral in which all of the four sides have the exact same length. In this case, since the sides UA and DA are 4 inches each, the sides QU and QD  will also have the same length.  

Also, the opposite sides are parallel, so we will have two sets of parallel sides with the same length.

The opposite angles in the rhombus are the same, so we would have two sets of opposite angles with the same values.