Question

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.

Answer 1

ABCD must be a paralellogram

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).