Mathematics

# Difference between Parallelogram and Trapezium

A parallelogram is a four-sided shape where opposite sides are parallel, and the opposite angles are congruent. In contrast, a trapezium is a four-sided shape that has one pair of parallel sides (the bases) and two non-parallel sides (the legs). The opposite angles of a trapezium are not congruent. The lengths of the bases can be different or equal but the opposite sides are not congruent. A rectangle is a common example of a parallelogram while a square is not a trapezium as all angles are right angles.

## What is a Parallelogram?

A parallelogram is a four-sided geometric shape where opposite sides are parallel to each other. This means that if two sides are parallel, so are the other two sides. The opposite angles of a parallelogram are also congruent. A common example of a parallelogram is a rectangle, which has all angles as right angles (90 degrees).

## What is a Trapezium?

A trapezium is a four-sided geometric shape that has one pair of parallel sides (the bases) and two non-parallel sides (the legs). The opposite angles of a trapezium are not congruent. The lengths of the bases can be different or equal but the opposite sides are not congruent.

## Overview

From the definitions of these two shapes, it is clear that while both are four-sided shapes, they have a different number of parallel sides. A parallelogram has opposite sides that are parallel, while a trapezium has one pair of parallel sides and the other two sides are non-parallel.

To further understand the difference between a parallelogram and a trapezium, one can consider the properties of opposite sides and angles. In a parallelogram, opposite sides are parallel and opposite angles are congruent. In a trapezium, one pair of opposite sides is parallel and the other pair of opposite sides is non-parallel and opposite angles are not congruent.

Here are ten key points to remember:

1. A parallelogram is a four-sided shape where opposite sides are parallel.
2. A trapezium is a four-sided shape that has one pair of parallel sides and two non-parallel sides.
3. The opposite angles of a parallelogram are congruent.
4. The opposite angles of a trapezium are not congruent.
5. A rectangle is a common example of a parallelogram.
6. A trapezium can have bases of different lengths.
7. The parallel sides of a trapezium are referred to as the bases.
8. A square is not a trapezium as all angles are right angles.
9. The non-parallel sides of a trapezium are called the legs.
10. A parallelogram is a special case of a trapezium where the bases are congruent.

## Conclusion

In conclusion, a parallelogram and a trapezium are both four-sided geometric shapes, but they have different properties. A parallelogram has opposite sides that are parallel and opposite angles are congruent, while a trapezium has one pair of parallel sides and two non-parallel sides, and opposite angles are not congruent.

A rectangle is a common example of a parallelogram and a square is not a trapezium as all angles are right angles. Understanding the differences and similarities between these shapes is crucial to correctly identify them in mathematical and real-world problems.