A parallelogram is a rhombus if and only if which condition holds?

• A. All angles are right angles
• B. Opposite sides are parallel
• C. Diagonals are perpendicular
• D. All four sides have the same length

Answer: (D)

A rhombus is a parallelogram with all sides the same length. So the defining test for a parallelogram to be a rhombus is that every side is equal in length. If you have a parallelogram where all four sides are equal, it fits the definition of a rhombus; and conversely, a rhombus certainly has all sides equal. This makes the condition both necessary and sufficient. The other ideas—having right angles, or focusing on the diagonals—describe other shapes or general properties and don’t single out the rhombus as clearly as the equal-sides condition.