Properties of Quadrilateral

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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

Introduction to Quadrilateral
Types of Quadrilateral
Properties of Quadrilateral
Parallelogram and its Theorems
Rectangle and its Theorems
Square and its Theorems
Rhombus and its Theorems
Trapezoid (Trapezium)and its Theorems
Kite and its Theorems
Mid Point Theorem

8th grade math
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