Some Special Parallelograms Class 8 Notes | EduRev

Class 8 Mathematics by VP Classes

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Class 8 : Some Special Parallelograms Class 8 Notes | EduRev

The document Some Special Parallelograms Class 8 Notes | EduRev is a part of the Class 8 Course Class 8 Mathematics by VP Classes.
All you need of Class 8 at this link: Class 8

SOME SPECIAL PARALLELOGRAMS
1. Rectangle
A rectangle is a parallelogram in which each angle is a right angle.
In rectangle,
Some Special Parallelograms Class 8 Notes | EduRev
(i) The opposite sides are equal and parallel,
(ii) Opposite angles are equal,
(iii) Diagonals ae equal,
(iv) Diagonals bisect each other.
Note: A rectangle is an equiangular figure but not an equilateral one.

2. Rhombus 
Arhombus is a parallelogram in which all four sides are equal.
In a rhombus, 

Some Special Parallelograms Class 8 Notes | EduRev

(i) Opposite sides are parallel,
(ii) All sides are equal,
(iii) Opposite angles are equal,
(iv) Diagonals bisect each other at right angles. 

3. Square 
A parallelogram having all of its sides equal and measure of each angle being 90°, is called a square.
In a square,

Some Special Parallelograms Class 8 Notes | EduRev

(i) All four sides are equal,
(ii) Opposite sides are parallel,
(iii) Each angle being equal to 90°,
(iv) The diagonals are equal,
(v) The diagonals bisect each other at right angles.
Note: A square is an equilateral and equiangular quadrilateral. Therefore it is called a regular polygon.

 

SUM OF THE MEASURES OF THE EXTERIOR ANGLES OF A POLYGON
Whatever be the number of sides of a polygon, the sum of the measures of its exterior angles is always 360°.
For example:
(a)
Some Special Parallelograms Class 8 Notes | EduRev
a + ∠b + ∠c + ∠d + ∠e = 360°

(b)
Some Special Parallelograms Class 8 Notes | EduRev
a + b + c + d + e + f = 360°

Example 1. Find the measure of x in the figure.

Some Special Parallelograms Class 8 Notes | EduRev

Solution: 
∵ Sum of all the exterior angles of a quadrilateral = 360°
∴ x + 65° + 115° + 110° = 360°
or
x + 290° = 360°
or    
x = 360° – 290° = 70°

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