Parallelogram vs. Rhombus

Main Difference

The main difference between Parallelogram and Rhombus is that the Parallelogram is a quadrilateral with two pairs of parallel sides and Rhombus is a quadrilateral in which all sides have the same length

• Parallelogram

  In Euclidean geometry, a parallelogram is a simple (non-self-intersecting) quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure. The congruence of opposite sides and opposite angles is a direct consequence of the Euclidean parallel postulate and neither condition can be proven without appealing to the Euclidean parallel postulate or one of its equivalent formulations.

  By comparison, a quadrilateral with just one pair of parallel sides is a trapezoid in American English or a trapezium in British English.

  The three-dimensional counterpart of a parallelogram is a parallelepiped.

  The etymology (in Greek παραλληλ-όγραμμον, a shape “of parallel lines”) reflects the definition.

• Rhombus

  In Euclidean geometry, a rhombus (◊) (plural rhombi or rhombuses) is a simple (non-self-intersecting) quadrilateral whose four sides all have the same length. Another name is equilateral quadrilateral, since equilateral means that all of its sides are equal in length. The rhombus is often called a diamond, after the diamonds suit in playing cards which resembles the projection of an octahedral diamond, or a lozenge, though the former sometimes refers specifically to a rhombus with a 60° angle (see Polyiamond), and the latter sometimes refers specifically to a rhombus with a 45° angle.

  Every rhombus is a parallelogram and a kite. A rhombus with right angles is a square.

• Rhombus (noun)

  a quadrilateral all of whose sides have the same length.