SOME SPECIAL PARALLELOGRAMS
A rectangle is a parallelogram in which each angle is a right angle.
(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.
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.
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°.
∠a + ∠b + ∠c + ∠d + ∠e = 360°
∠a + ∠b + ∠c + ∠d + ∠e + ∠f = 360°
Example 1. Find the measure of x in the figure.
∵ Sum of all the exterior angles of a quadrilateral = 360°
∴ x + 65° + 115° + 110° = 360°
x + 290° = 360°
x = 360° – 290° = 70°