Parallelogram - Definition with Examples

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What is Parallelogram?

A parallelogram is a special type of quadrilateral that has equal and parallel opposite sides. 

The given figure shows a parallelogram ABCD which as AB parallel to CD and AD parallel to BC.

Also, AD = BC and AB = CD.

parallelogram

 

We also see a lot of parallelogram like shapes and objects around us. 

 

Properties of parallelogram
 
Properties of parallelogram 1

 The opposite sides of a parallelogram are parallel to each other.

 Here, AB ∥ CD and AD ∥ BC

 

Properties of parallelogram 1

 The opposite sides of a parallelogram are equal in length.

 Here, AB = CD and AD = BC

 

Properties of parallelogram 4

 The opposite angles of a parallelogram are equal in measure.

 Here, Angle A = Angle C and

 Angle B = Angle D.

Properties of parallelogram 4

 Adjacent angles of a parallelogram add up to 180°

 Here, Angle A + Angle B = 180°

 Angle B + Angle C = 180°

 Angle C + Angle D = 180°

 Angle D + Angle A = 180°

Properties of parallelogram 5

 Diagonals of a parallelogram bisect each other.

 Here AC and BD bisect each other.

 

Types of a parallelogram

There are three special types of a parallelogram.

 1. Rhombus: A parallelogram in which all sides are equal.

Rhombus parallelogram

Here AB = BC = CD = DA.  ABCD is a rhombus.
 

 2. Rectangle: A parallelogram in which all angles are right angles and the diagonals are equal.

rectangle parallelogram 

Here all angles are right angles. Diagonals PN and OM are equal.
 

 3. Square: A parallelogram with all equal sides and all angles equal to 90 degrees. The diagonals of a square are also equal.

square parallelogram

Here all sides are equal and all the angles are right angles.

Diagonals AC and BD are equal.

  Fun Facts

  • The term ‘parallelogram’ is derived from Middle French ‘parallélogramme’, Late Latin ‘parallelogrammum’ and Greek ‘parallelogrammon’ which means “bounded by parallel lines”.

 

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