Question

Can you tell me all the properties of all quadrilaterals........

Answer 1

There are different properties of quadrilateral. On the basis of it we can recognize what type of quadrilateral is this.

Properties of Quadrilateral : 

Parallelogram : 

Properties : a) The opposite sides are equal. ( AB = DC and AD = BC )
b) The opposite angles are equal.( ∠A = ∠C and ∠ B = ∠D) 
c) The adjacent angles are supplementary.( ∠A + ∠B= 180)
d) The diagonals bisect each other.( AO = OC and BO = OD).

2) Rectangle : A rectangle is a parallelogram in which each angle is 900.


Properties: a) The opposite sides are equal and parallel. ( AB = DC and 
AD = BC also AB || CD and AD || BC)
b) Each angle is a right angle.( ∠A = ∠B = ∠ C = ∠D = 900) 
c) Diagonals are equal.(AC = BD)
d) Diagonals bisect each other. (AO = OC and BO = OD)

3) Square : A square is a parallelogram with all sides equal and
all angles are 900

Properties : a) All sides are equal.(AB = BC= CD = DA)
b) Each angle is right angle.
c) Diagonal are equal and bisect each other at right angle.

4) Rhombus : Rhombus is a parallelogram with all sides equal and parallel.

Properties : a) All sides are equal. (AB = BC= CD = DA)
c) Opposite angles are equal.
d) Adjacent angles are supplementary( adds up to 180)
e) Diagonals bisect each other at right angle.

5) Trapezoid : It is a quadrilateral with only one pair of parallel sides. 
AB || CD
Properties : a) Adjacent angles are supplementary.( ∠1 + ∠2 = 180 and 
∠3 + ∠4 = 180)
Note : If non parallel sides (AD = BC) are equal then the trapezoid is called Isosceles Trapezoid.

6) Kite : 
Properties : a) Adjacent sides are equal.(AB = AD and BC = CD)
b) Diagonals intersect each other at right angle.( AC bisect BD)
c) BO = OD