Quadrilaterals

                      Quadrilaterals

°What is quadrilateral? 

   A plane, closed figure bounded by four line segments is called quadrilateral. There are different types of quadrilaterals, they are trapezium, parallelogram, rhombus, rectangle, square. 

•What is the sum of all the interior angles of a quadrilateral? 

The sum of all the interior angles of a quadrilateral is 360 degree. 

           Important Formulae

                     Special quadrilaterals

Parallelogram- A parallelogram is a quadrilateral with both pairs of opposite sides parallel. 

Important points -

Opposite sides of a parallelogram are equal

Opposite angles of a parallelogram are equal

The diagonals of a parallelogram bisect one another. 

Each diagonal divides it into two congruent triangles. 

The opposite sides and angles of a parallelogram are equal.

The diagonals of a parallelogram bisect each other. 

Rectangle- a parallelogram in which all four angles are right angles is a rectangle. 

Important points - 

All angles of a rectangle are right angles. 

The diagonals of the rectangle are equal. 

Rhombus- A parallelogram whose all four sides are equal is a rhombus. 

Important points - 

Opposite angles of a rhombus are equal. 

Diagonals of a rhombus bisect each other. 

All the sides of a rhombus are equal. 

The diagonals of a rhombus cut at right angles. 

Note - The diagonals of a rhombus are not equal. 

Square- A parallelogram in which all four sides are equal and all four angles are right angle is a square. 

Important points - 

All the sides of a square are equal. 

The diagonals of a square are equal and bisect each other at right angles. 

The angle which a diagonal makes with a side of the square is 45° . 

Trapezium- A quadrilateral with exactly one pair of parallel sides is a trapezium. 

Isosceles trapezium - A trapezium in which two non parallel sides are equal each pair of base angles are equal. 

Kite - A quadrilateral in which the two pairs of adjacent sides are equal is a kite. 

Important point 

The diagonals are perpendicular to each other.

Arrowhead - a kite with one reflex angle is called an arrowhead. 

 

Isosceles Trapezium 

The diagonals are equal. 

The co-interior angles are supplementary. 

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