** Diamond, Rhombus vs Trapezoid **

Diamond, Rhombus, and Trapezoid are all * quadrilaterals*, which are polygons with four sides. While rhombus and trapezium are properly defined in mathematics, diamond (or diamond shape) is a layman’s term for rhombus.

**Rhombus and Diamond**

A quadrilateral with all sides equal are in length is known as a rhombus. It is also named as an * equilateral quadrilateral*. It is considered to have a diamond shape, similar to the one in the playing cards. Diamond shape is not a precisely defined geometrical entity.

Rhombus is a special case of the * parallelogram*. It can be considered as a parallelogram with equal sides. The square can be considered as a special case of the rhombus, where the internal angles are right angles. In general, a rhombus has the following special properties

*• All four sides are equal in length. (AB=DC=AD=BC)*

*• The diagonals of the rhombus bisect each other at right angles; diagonals are perpendicular to each other,*

in addition to the following properties of a parallelogram.

*• *Two pairs of opposing angles are equal in size. (DÂB = BĈD, A* ̂*DC=A* ̂*BC)

*• *The adjacent angles are supplementary DÂB+A* ̂*DC = A* ̂*DC+B* ̂*CD = B* ̂*CD+A* ̂*BC = A* ̂*BC+D* ̂*AB = 180° = π rad

*• *A pair of sides, which are opposing each other, is parallel and equal in length. ( AB=DC & AB∥DC)

*• *The diagonals bisect each other (AO=OC, BO=OD)

*• *Each diagonal divides the quadrilateral into two congruent triangles. (*∆*ADB ≡ *∆*BCD, *∆*ABC ≡ *∆*ADC)

*• *The diagonals bisect the two opposite internal angles.

Area of the rhombus can be calculated using the following formula.

*Area of rhombus = ½ (AC × BD)*

**Trapezoid (Trapezium)**

Trapezoid is a convex quadrilateral where at least two sides are parallel and unequal in length. The parallel sides of the trapezoid are known as the * bases* and the other two sides are called the

*.*

**legs**Following are main characteristics of trapezoids;

*• *If the adjacent angles are not on the same base of the trapezoid, they are supplementary angles. i.e. they add up to 180° (BA ̂D+AD ̂C = AB ̂C+BC ̂D = 180°)

*• *The two diagonals of the trapezium intersect at the same ratio (ratio between the section of the diagonals are equal).

*• *If a and b are bases and c,d are legs, the *lengths of the diagonals** are given by *

Area of the trapezoid can be calculated using the following formula.

Read the **Difference Between Parallelogram and Trapezoid**

**What is the difference between Diamond, Rhombus and Trapezoid?**

• Rhombus and Trapezoid are well-defined mathematical objects while diamond shape is a layman’s term. Each shape has four sides, and diamond shape refers to a rhombus.

• Rhombus has equal sides, with opposing sides parallel to each other. Trapezoid has unequal sides in general, with two sides parallel to each other. Only the legs of the trapezoid can be equal.

• Any diagonal of the rhombus separates the rhombus into two congruent triangles. The triangles formed by the diagonals of the trapezoid are not necessarily congruent.

• Diagonals of the rhombus intersect each other at right angles while diagonals of the trapezoid are not necessarily perpendicular to each other.

• Diagonals of the rhombus bisect each other while diagonals of the rhombus intersect at the same ratio.

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