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**SOME SPECIAL PARALLELOGRAMS****1. Rectangle**

A rectangle is a parallelogram in which each angle is a right angle.

In rectangle,

(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,

(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,

(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)****∠****a + ∠b + ∠c + ∠d + ∠e = 360°**

**(b)****∠****a + ∠b + ∠c + ∠d + ∠e + ∠f = 360°**

∵ 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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