Mathematics

# Parallelogram vs Rhombus vs Trapezium

A parallelogram, Rhombus, and Trapezium are all four-sided geometric shapes that have their own unique characteristics. However, many people tend to confuse these shapes with one another. This article aims to provide a comprehensive overview of these shapes, including their definitions, similarities, and differences.

## 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 Rhombus?

A rhombus is a specific type of parallelogram where all four sides have equal length. This means that opposite sides are parallel and congruent. The opposite angles of a rhombus are also congruent. A square is a specific type of rhombus where all four angles are right angles (90 degrees).

## What is a Trapezium?

A trapezium is a four-sided geometric shape that has one pair of parallel sides and the other two sides are non-parallel. The opposite angles of a trapezium are not congruent. The parallel sides of a trapezium are referred to as the bases and the non-parallel sides are called the legs.

Now, let’s take a look at a comparison table to understand the similarities and differences between these shapes.

ShapeOpposite SidesOpposite Angles
ParallelogramParallelCongruent
RhombusParallel & CongruentCongruent
TrapeziumOne pair parallelNot Congruent

As we can see from the table above, all three shapes have parallel opposite sides, but the rhombus is the only one where the opposite sides are also congruent. In terms of opposite angles, parallelograms and rhombus have congruent opposite angles, while trapezium does not.

Here are ten key points to remember about these shapes:

1. A parallelogram is a four-sided shape where opposite sides are parallel.
2. A rhombus is a specific type of parallelogram where all four sides have equal length.
3. A trapezium is a four-sided shape that has one pair of parallel sides and the other two sides are non-parallel.
4. The opposite angles of a parallelogram are congruent.
5. The opposite angles of a rhombus are also congruent.
6. The opposite angles of a trapezium are not congruent.
7. A rectangle is a common example of a parallelogram.
8. A square is a specific type of rhombus where all four angles are right angles.
9. The parallel sides of a trapezium are referred to as the bases and the non-parallel sides are called the legs.
10. A square is a parallelogram and rhombus at the same time as it has all sides congruent and all angles as right angles.

## Conclusion

In conclusion, a parallelogram, rhombus, and trapezium are all four-sided geometric shapes that have their own unique characteristics. A parallelogram is defined as having opposite sides that are parallel, while a rhombus is a specific type of parallelogram where all four sides have equal lengths. A trapezium, on the other hand, has one pair of parallel sides (the bases) and two non-parallel sides (the legs). it’s essential to note that while a parallelogram is not always a rhombus, a square which is a specific type of rectangle and has all four sides congruent is both a parallelogram and a rhombus.