Quadrilaterals

WHAT IS A QUADRILATERAL? Any figure with four vertices and four

sides is known as a quadrilateral. For e.g.:- Parallelogram Rectangle Square Trapezium

Square trapezium

rectangle

Angle sum property of a quadrilateralThe sum of all the angles of a quadrilateral is 360˚. This is the angle sum property of a quadrilateral.

Parallelogram If both pairs of opposite sides of a

quadrilateral are equal and parallel, then it is a parallelogram.

Characteristics of a parallelogram (1)Opposite sides are equal. (2)Opposite angles are equal. (3)The diagonals of a Parallelogram

bisects it into two congruent triangles.

Rectangle It is a parallelogram with one

angle=90˚.

Rhombus It is a parallelogram having all sides

equal.

Square It is a rhombus where one angle is 90˚

kite It is a quadrilateral with two pairs of

equal opposite sides.

THEOREMS

A diagonal of a parallelogram divides it into two congruent triangles.

In a parallelogram opposite sides are equal.

If each pair of opposite sides of a quadrilateral are equal, the it is a parallelogram.

In a parallelogram opposite sides are equal.

If in a quadrilateral, each pair of opposite angles is equal, the it is a quadrilateral.

The diagonals of a parallelogram bisects each other.

If the diagonals of a quadrilateral bisect each other, then it is a parallelogram.

A quadrilateral is a parallelogram, If a pair of opposite sides is equal and parallel.

Mid Point Theorem The line segment joining the midpoints

of the two sides of a triangle is parallel to the third side.

The line drawn through the mid point of one side of a triangle parallel to the other side bisects the third side.