Quadrilateral – Definition – Properties

There are kinds of quadrilaterals, based on the sides and angles. 

1. Parallelogram

2  Rectangle

3. Square

4. Rhombus

5. Trapezium

6. kite

1.                       Parallelogram

A Parallelogram is a quadrilateral, whose both pairs of opposite sides are parallel and equal in length.

In above figure ABCD is a Parallelogram, whose one pair of sides AB and CD and other pair, AC and BD,  both are Parallel.
 “∥” is the sign of Parallel and read as Parallel to, 
                   In this Parallelogram

                     AB∥CD and AC∥BD

   read as AB Parallel to CD and AC parallel to BD.

AB = CD

2.                       Rectangle

A Rectangle is a quadrilateral, whose every internal angle is right angle or 90 degree and both pairs of opposite sides are parallel and equal in length.

In above figure ABCD is a rectangle, whose one pair of sides AB and CD and other pair of sides AC and BD both are Parallel and equal.

                           AB∥CD and AC∥BD

                        AB = CD and AC = BD

                  ∠A, ∠B  ∠C, and ∠D are 90⁰

3.                               Square

A Square is a quadrilateral, whose every internal angle is right angle or 90 degree, four sides are equal in length and both pairs of opposite sides are parallel.

A Square is a quadrilateral, whose every internal angle is right angle or 90 degree, four sides are equal in length and both pairs of opposite sides are parallel.

In above figure ABCD is a square, whose one pair of sides AB and CD and other pair of sides AC and BD both are Parallel and all four sides AB, CD, AC and BD are equal.

 Thus,                 AB∥CD and AC∥BD

                        AB = CD = AC = BD

                  ∠A, ∠B  ∠C, and ∠D are 90⁰

                  ∠A = ∠B = ∠C = ∠D = 90⁰

4.                             Rhombus

A rhombus is a quadrilateral, whose four sides are equal in length, both pairs of opposite sides are parallel and opposite angles are equal.   

A rhombus is a quadrilateral, whose four sides are equal in length, both pairs of opposite sides are parallel and opposite angles are equal.   

In above figure ABCD is a rhombus, whose one pair of sides AB and CD and other pair of sides AC and BD both are Parallel and all four sides are equal.

 Thus,                 AB∥CD and AC∥BD

                        AB = CD = AC = BD

                     ∠A = ∠D  and  ∠C = ∠B 

5.                              Trapezium

Trapezium is quadrilateral whose a pair (base) of sides are parallel.

In above figure ABCD is a trapezium whose one pair of sides AB and CD are Parallel.
                                 AB ∥ CD

6.                              Kite

A kite is a quadrilateral whose two pairs of adjacent(touching) sides that are congruent(equal in length).

In above figure ABCD is a kite whose two pair of sides

AB equal to AD and BC equal to DC.
                                 AB = AD and BC = DC