Given quadrilateral abcd, if diagonals ac and bd bisect each other, and angle abc=91°, but you know nothing about any lengths in the diagram, what special figure must abcd be? a rhombus or a parallelogram? how do you know.

ABCD must be a paralellogram

Step-by-step explanation:

In parallelogram, rectangle, square and rhombus the diagonals bisect each other. Since angle ABC=91°, then this quadrilateral cannot be rectangle and cannot be square, because rectangle and square have all right angles (90°).

If diagonals of a quadrilateral bisect each other, then quadrilateral is parallelogram. A rhombus is a parallelogram with all congruent sides.

You know nothing about any lengths in the diagram, then you can state that this quadrilateral is parallelogram (always) and can be rhombus (sometimes).