Properties of parallelogram and its Types
A parallelogram is a special kind of quadrilateral in which both pairs of opposite sides are parallel. In fig. 1 given below, AD||BC and AB||CD .
The four basic properties of parallelogram are:
There are three special types of parallelogram, they are:
Let us discuss these special parallelograms one by one.
Rectangle is a special case of parallelogram in which measure of each interior angle is \( 90^\circ \)
The path which surrounds a two-dimensional object is known as its perimeter. The two-dimensional space occupied by an object is known as its area. A rectangle with length l units and breadth as b units has perimeter equal to 2( l + b) units and its area is equal to \( l \times b \)
Fig. 2 shown above represents a rectangle in which all angles are right angles and opposite sides are equal.
Since a rectangle is a parallelogram, it inherits all the properties of parallelogram along with some special properties which differentiates it from other parallelograms:
Properties of rectangle:
A parallelogram in which all four sides are equal in length is known as a rhombus. A rhombus is an equilateral quadrilateral. By equilateral quadrilateral, we mean a quadrilateral with all sides equal. Every rhombus is a parallelogram since it has both pairs of opposite sides parallel. When all the sides of a kite become equal in length, then that kite becomes a rhombus as sides are of equal length and diagonals are perpendicular to each other. Hence, every rhombus is also a kite.
Fig. 3 represents a rhombus with sides AB = BC = CD = DA and diagonals intersecting at right angles.
Since a rhombus is a parallelogram, all the properties of a parallelogram are applicable to it.
Properties of Rhombus:
Geometrically, polygons are related with their duals i.e. vertices of one polygon correspond to sides of another polygon. Rhombus is the dual polygon of rectangle and vice- versa. By joining mid points of sides of rectangle a rhombus is formed and vice-versa. This could be understood through the table given below:
|Equiangular quadrilateral- All angles are equal||Equilateral quadrilateral- All sides are equal|
|Opposite sides are congruent||Opposite angles are congruent|
|Point of intersection of diagonals is equidistant from vertices therefore it circumscribes a circle.||Point of intersection of diagonals is equidistant from sides therefore it inscribes a circle.|
|Length of diagonals is equal||Intersection of diagonals is at equal angles|
|Opposite sides are bisected by its axis of symmetry||Opposite angles are bisected by its axis of symmetry|
Table1: Duality of Rectangle and Rhombus
Square: A parallelogram which has properties of both a rhombus and a rectangle. A square is a parallelogram with equal sides and one of its interior angles as right angle.
Fig. 4 depicts a square in which measure of each interior angle is \( 90^\circ \)
Properties of Square:
Here are different types of Parallelogram and their properties. For more on parallelograms watch the video.’
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