Forms of Quadrilaterals

Forms of Quadrilateral

What is Quadrilateral?

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, as is BD.

Properties of a quadrilateral:

Four sides (or edges)
Four vertices (or corners).

The interior angles add up to 360 degrees

Forms of Quadrilateral:

Parallelograms

Quadrilaterals are called parallelograms if both pairs of opposite sides are equal and parallel to each other.  Different parallelograms and their properties are described below.

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

Rectangle

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



Square

A square has equal sides and every angle is a right angle (90°)
Also opposite sides are parallel.
A square also fits the definition of a rectangle (all angles are 90°), and a rhombus (all sides are equal length).

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

Trapezium

A trapezium has one pair of opposite sides parallel

A regular trapezium has non-parallel sides equal and its base angles are equal, as shown in the diagram

Kite

Two pairs of adjacent sides of a kite are equal in length
One pair of opposite angles (the ones that are between the sides of unequal length) are equal in size.
One diagonal bisects the other.
Diagonals intersect at right angles.