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A quadrilateral is a 2-dimensional closed shape with four straight sides. E.g. The shape ABCD shown here is a quadrilateral.

A line segment drawn from one vertex of a quadrilateral to the opposite vertex is called a diagonal of the quadrilateral. AC is a diagonal of quadrilateral ABCD, so is BD.

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There are seven types of quadrilaterals that can be divided into two groups: parallelograms and other quadrilaterals.

1. Parallelograms

Quadrilaterals are called parallelograms if both pairs of opposite sides are equal and parallel to each other.

Different parallelograms and their properties.

a) Parallelogram
Opposite sides of a parallelogram are parallel and equal in length. Opposite angles are equal in size.

b) Rectangle
Opposite sides of a rectangle are parallel and equal in length, All angles are equal to 90°.

c) Square
Opposite sides of a square are parallel and all sides are equal in length, All angles are equal to 90°.

d) Rhombus
All sides of a rhombus are equal in length,
Opposite sides are parallel,
Opposite angles of a rhombus are equal,
The diagonals of a rhombus bisect each other at right angles.

Rectangles, squares and rhombuses are parallelograms.

a) Trapezium
A trapezium has one pair of opposite sides parallel.
A regular trapezium has non-parallel sides equal and its base angles are equal.

b) Kite
Two pairs of adjacent sides of a kite are equal in length
One pair of opposite angles are equal in size.
One diagonal bisects the other.
Diagonals intersect at right angles.

An irregular quadrilateral does not have any special properties.

Angle Sum of a Quadrilateral is 360 degrees

Points to remember

A square has got four sides of equal length and 4 right angles (right angle = 90 degrees).

A Rhombus has got four sides of equal length and opposite sides are parallel and angles are equal.

The rectangle contains four right angles (an angle of 90˚). It has got two pairs of equal length sides

A parallelogram is a rectangle that has been pushed over. Opposite sides are the same length and they are parallel.

A trapezium as got one pair of parallel sides.

A kite as got two pairs of sides next to each other that have equal length.

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