Quadrilaterals

Some special type of Quadrilaterals

Quadrilaterals are the polygons having four sides. Parallelogram, rectangle, square, rhombus, trapezium, and kite have some special properties. So, they are called special types of a quadrilateral. Some types of quadrilateral are as follows

1. Parallelogram
   
   

   

   

   
   Its opposite sides are equal and parallel.
   \(\therefore\) AB= DC and AB//DC, AD = BC and AD//BC.
   Its opposite angles are equal.
   \(\therefore\) \(\angle\)A = \(\angle\)C and \(\angle\)B = \(\angle\)D
   Its diagonal bisect each other.
   \(\therefore\) Diagonals AC and BD bisect each other ar O.
   i.e AO = OC and BO = OD.
2. Rectangle
   
   

   

   

   
   Its opposite sides are equal and parallel.
   \(\therefore\) AB = DC and AB//DC, AD = BC and AD//BC.
   Its all angles are equal andeach of them is 90°.
   \(\angle\)A = \(\angle\)B = \(\angle\)C = \(\angle\)D = 90°.
   Its diagonalsare equal and they bisect each other.
   \(\therefore\) Diagonals AC = BD, AO = OC and BO = OD.
3. Square
   
   

   

   
   

   

   ts all sides are equal.
   \(\therefore\) AB = BC = CD = DA
   Its all angles are equal and they are 90°.
   \(\therefore\) \(\angle\)A = \(\angle\)B = \(\angle\)C = \(\angle\)D = 90.
   Its diagonal are equal and they bisect each other at right angle.
   \(\therefore\) AC = BD and they bisect each other at O at a right angle.
   i.e AO = OC, BO = OD and BD⊥AC at O.
4. Rhombus
   Its all sides are equal and opposite sides are parallel.
   

   

   
   \(\therefore\) AB = BC = CD = DA and AB//DC, AD//BC
   Its opposite angles are equal.
   \(\therefore\) \(\angle\)A = \(\angle\)C and \(\angle\)B = \(\angle\)D
   Its diagonals are not equal but they bisect each other at right angle.
   \(\therefore\) AC and BD bisect each other at O at right angle.
   i.e AO = OC, BO = OD and BD⊥AC at O.
5. Trapezium
   
   

   

   
   Its any one pair of opposite sides are parallel.
   \(\therefore\) AB//DC.
6. Kite
   

   

   
   Its particular pairs of adjacent sides are equal.
   AB = AD and BC = DC
   The opposite angles formed by each pair of unequal adjacent sides are equal.
   \(\angle\)ABC = \(\angle\)ADC
   Diagonals intersect each other at O at a right angle.
   i.e BD⊥AC at O.

Things to remember

• Opposite sides of a parallelogram are equal and parallel. 
• The sides of rhombus are equal and opposite sides are parallel.
• The particular pairs of adjacent sides are equal.

• It includes every relationship which established among the people.
• There can be more than one community in a society. Community smaller than society.
• It is a network of social relationships which cannot see or touched.
• common interests and common objectives are not necessary for society.

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