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.