Name the different types of
parallelograms. Draw their rough
diagrams and write their properties.
Answers
Answer:
घोक्सजधफबसाफक्सग्सी्सीछालूरसेबेहजेजेज
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 .
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:
- The four basic properties of parallelogram are:Opposite sides of a parallelogram are equal
•Opposite angles of parallelogram are equal
•Diagonals divide the parallelogram
into two congruent triangles
•Diagonals bisect each other
There are three special types of parallelogram, they are:
•Rectangle
•Rhombus
•Square
Rectangle:
Rectangle:Rectangle is a special case of parallelogram in which measure of each interior angle is
Rectangle:Rectangle is a special case of parallelogram in which measure of each interior angle is 90∘. It is an equiangular quadrilateral.By equiangular quadrilateral, it means that all the interior angles are equal in magnitude. Since the measure of each angle is
Rectangle:Rectangle is a special case of parallelogram in which measure of each interior angle is 90∘. It is an equiangular quadrilateral.By equiangular quadrilateral, it means that all the interior angles are equal in magnitude. Since the measure of each angle is 90∘,therefore sum of its opposite angles is supplementary and hence it is a cyclic quadrilateral i.e. all its vertices lie on circumference of a circle.
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
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×bsq. units.
Fig. 2 shown above represents a rectangle in which all angles are right angles and opposite sides are equal.
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:
•Measure of each interior angle is 90∘
•Opposite sides are equal
•Diagonals are congruent
•Each diagonal is angle bisector of opposite
angle
Rhombus:
Rhombus: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.
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.
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:
•All sides are congruent
•Diagonals bisect each other at right angles
•Opposite angles are equal and each diagonal is angle bisector of opposite angle
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∘ and AB = BC = CD = DA.
Properties of Square:
•All sides are equal in length
•Each interior angle is right angle
•Length of diagonals is equal
•Diagonals are perpendicular bisectors of each other
•Every square is a parallelogram in which diagonals are congruent and bisect the angles
•Every square is a rectangle and a rhombus
