Last modified on August 3rd, 2023

chapter outline


Rhombus vs Parallelogram

Rhombuses and parallelograms both belong to the family of quadrilaterals. All types of quadrilaterals have some properties that bring them under the same category. However, each member of the family is different from the other in some aspects. Here we will discuss the differences between a rhombus and a parallelogram.

Let us compare the figure of a rhombus and a parallelogram below.

Rhombus vs Parallelogram

What is the Difference between a Rhombus and a Parallelogram

SIDESAll sides are congruentOpposite sides are equal, adjacent sides are unequal
DIAGONALSBisect each other at 90° and are equalBisect each other but not at 90° and are unequal
PERIMETERIt is given by P = 4s, where ‘s’ is any sideIt is given by 2(a + b), where a and b are the side and the base respectively
AREAIt is given by  (d1 × d2)/2 where d1 and d2 are the length of the two diagonalsIt is given by b × h where b and h represent the base and the height respectively
RELATIONA rhombus is a parallelogram since it satisfies all the properties a parallelogram exhibitsA parallelogram is not a rhombus as it does not satisfy the congruency of all its sides which a rhombus does

Similarities Between a Rhombus and a Parallelogram

  • Have four sides
  • Opposite sides equal and parallel
  • Opposite angles equal
  • Diagonals bisecting each other

Is a Rhombus a Parallelogram

YES! Remember, a parallelogram has 2 pairs of sides that are mutually opposite, parallel, and equal, and 2 diagonals mutually bisecting. Doesn’t a rhombus also satisfy this definition? YES. A rhombus satisfies all the properties of a parallelogram. So a rhombus is a parallelogram. Therefore, we can consider a rhombus as a subset of a parallelogram.

However, is a rhombus always a parallelogram?

YES! A rhombus is always a parallelogram.

A rhombus exhibits all the properties of a parallelogram. Also, it has all its sides congruent. Its all-sides congruency makes the diagonals bisect perpendicularly. Thus, we often consider a rhombus as a slanting square and a parallelogram as a slanting rectangle.

How to Prove a Parallelogram is a Rhombus

To prove: ABCD is a rhombus


Given: ABCD is a parallelogram



∠DEA = 90°

1∠AED ≅ ∠BECVertical angles are ≅
2Δ AED ≅ ΔBECAngle – Angle Side (AAS) Postulate
3AE ≅ ECCorresponding Parts of Congruent Triangles (CPCTC) postulate
4DE ≅ EBCPCTC postulate
5AC ⊥ Bis BD BD ⊥ Bis ACDefinition of perpendicular bisector
6ABCD is a rhombusDefinition of rhombus
Hence Proved

Now think the other way round. Are parallelograms rhombuses?

NO. A parallelogram does not have all its sides congruent, unlike a rhombus.

Last modified on August 3rd, 2023

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