Types of Quadrilateral and their properties

Quadrilateral: A quadrilateral is a four-sided closed figure having four vertices, four angles, and two diagonals.

In the given figure ABCD is a quadrilateral 

Quadrilateral

The sum of four angles of the quadrilateral is always 360 º i.e ∠A+∠B+∠C+∠D=360º

Types of Quadrilateral 

There are six types of quadrilaterals based on their Properties. Let’s discuss them one -by-one 

1. Rectangle 

A Quadrilateral is knowns as Rectangle when its opposite sides are parallel and each angle measure is 90 º.In the given figure, ABCD is  a rectangle whose opposite sides are parallel i.e AB||CD and AD|| BC and each angle is a right angle 

Rectangle

Properties of Rectangle 

1. The opposite side of the Rectangle are parallel and equal 

2. Each angle of the Rectangle is a right angle 

3. The diagonal of a rectangle bisect each other and are equal in length 

2. Square 

Remember this: A square is a rectangle in which rectangle all sides are equal 

That’s why the definition of Square and Rectangle are the almost same 

A Quadrilateral is knowns as Rectangle when its opposite sides are parallel and each angle measure is 90 º.In the given figure ABCD is a square , Whose AB||CD and AD|| BC and each angle is a right angle 

Square

Properties of square 

  • The opposite sides of the square are parallel. 
  • All four sides of a square are equal whereas In a rectangle only the Opposite side are equal 
  • Each angle of the square is a right angle 
  • Diagonals of a square bisect each other at 90 º and are equal in size 

3. Parallelogram 

A quadrilateral is known as a Parallelogram(write as llgm )  when its opposite sides are parallel and opposite angles are equal.

In the given figure ,ABCD is a llgm whose opposite side is parallel AB||CD and AD|| BC and opposite angles are equal ∠A=∠C and ∠B=∠D 

Parallelogram

Properties of Parallelogram 

  • The opposite side of the parallelogram are parallel and equal 
  • Opposite angles of a parallelogram are equal 
  • Diagonal of llgm bisect each other but no are equal in length 
  • Pairs of adjacent angles are supplementary i.e 180º

4. Rhombus 

Note:Rhombus is a parallelogram in which all four sides are equal 

A quadrilateral is known as Rhombus when its opposite sides are parallel and opposite angles are equal . The difference between Rhombus and parallelogram is,

Rhombus all sides are equal whereas parallelogram has only opposite sides equal 

 

Properties of Rhombus 

  • All sides of a rhombus are equal 
  • opposite sides of a rhombus are parallel 
  • opposite angles of a rhombus are equal 
  • Diagonals of a rhombus bisect each other at a right angle  

You have noticed some similarity in these four quadrilaterals to each other because these are related to each other 

Notes: 

  • A square is a rhombus but a rhombus may not be a square 
  • A square is a rectangle but a rectangle may not be a square 
  • A square is a parallelogram but a parallelogram may not be a square 

5. Trapezium 

A quadrilateral is an as known a Trapezium whose one pair of sides are parallel and equal to each other. In the given figure, ABCD is a trapezium because AB||CD and AB=CD 

Trapezium

Properties of Trapezium 

  • One side of a trapezium is parallel and equal 
  • When non-parallel sides and base angle are equal, then it’s known as regular Trapezium 

6. Kite 

A quadrilateral is known as Kite whose two pairs of adjacent sides are equal  . In the given figure, ABCD is a kite because its adjacent sides are equal 

Image source: geometryhelp.net

Properties of kite 

  • Two pairs of adjacent sides are equal 
  • One pair of opposite angles are equal 
  • The longest diagonal bisect the shortest diagonal at the right angle 

 

 

 

 

 

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