Quadrilaterals

 

Different types of quadrilaterals are explained with their definition and properties along with the diagram.

1) Parallelogram


 

A quadrilateral is called a parallelogram, if both pairs of its opposite sides are parallel. In the adjoining figure, ABCD is a quadrilateral in which AB is parallel to DC and DC is parallel to BC AB ∥ DC and AD ∥ BC.

So, ABCD is a parallelogram.

2) Rhombus


 

A parallelogram having all sides equal is called a rhombus. In the adjoining figure, ABCD is a rhombus in which AB is parallel to DC, BC is parallel to BC and AB=BC+CD=DA AB ∥ DC, AD ∥ BC and AB = BC = CD = DA.

3) Rectangle


 

A parallelogram in which each angle is a right angle is called a rectangle. In the adjoining figure, ABCD is a quadrilateral in which AB is parallel to DC, AD is parallel to BC, Right angle B is parallel to Right angle B=Right angle C=Right angle D= 90.° AB ∥ DC, AD ∥ BC and ∠A = ∠B = ∠C = ∠D = 90°.

So, ABCD is a Rectangle.

4) Square


 

A parallelogram in which all the sides are equal and each angle measures 90° is called a square.

In the adjoining figure, ABCD is a quadrilateral in which AB is parallel to DC, AD is parallel to BC, AB=BC=CD=DA and Right angle A=Right angle B=Right angle C=Right angled=. 90°.

AB ∥ DC, AD ∥ BC, AB = BC = CD = DA and ∠A = ∠B = ∠ C = ∠D = 90°.

So, ABCD is a Square.

5) Trapezium

A quadrilateral having exactly one pair of parallel sides is called a trapezium. In the adjoining figure, ABCD is a quadrilateral in which AB is parallel to DC. AB ∥ DC.

So, ABCD is a Trapezium.

6) Isosceles Trapezium

A trapezium whose non-parallel sides are equal is called an isosceles trapezium. Thus, in the adjoining figure, ABCD will be an isosceles trapezium if AB is parallel to BC and AB=BC.

AD ∥ BC and AB = BC

7) Kite


 

A quadrilateral is called a kite if it has two pairs of equal adjacent sides but unequal opposite sides. In the adjoining figure, ABCD is a quadrilateral.

AB = AD, BC = DC, AD ≠ BC and AB ≠ DC.

So, ABCD is a Kite.