### Theory:

A trapezium or a trapezoid is a quadrilateral with a pair of parallel sides. A parallelogram has also be called a trapezoid as it has two parallel sides.

- The pair of parallel sides have called the base while the non-parallel sides are called the legs of the trapezium.
- The line segment that connects the midpoints of the legs of a trapezium is called the mid-segment.

Properties of a Trapezium:

- The diagonals of trapezium bisect each other.
- A Trapezium has two parallel sides and two non-parallel sides.
- A Trapezium has four unequal sides.
- Like other quadrilaterals, the sum of all the four angles of the trapezium is equal to 360 degrees.
- No sides, angles and diagonals of the trapezium are congruent.
- The length of the mid-segment is equal to 1/2 the sum of the parallel bases, in a trapezium.

The concept of the trapezium has highly used in various physics computations and other mathematical calculations.

**Trapezoid & Trapezium**

In the US and UK, Trapezoid and Trapezium have differentiated as below.

| Trapezoid | Trapezium |

US | A quadrilateral with a pair of parallel sides. | A quadrilateral with no parallel sides. |

UK | A quadrilateral with no parallel sides. | A quadrilateral with a pair of parallel sides. |