A quadrilateral is a two-dimension structure having four sides. Thus, a rectangle and a trapezoid are also quadrilaterals having prominent differences between them.
One may get confused between the two terms, and questions like these may arise in his/ her mind: What are the differences between their structures? Are both of them parallelogram? How do they differ in terms of diagonals and opposite sides?
Rectangle vs Trapezoid
The main difference between a rectangle and a trapezoid is that a rectangle is a four-sided parallelogram with two pairs of parallel and equal opposite sides and four right angles. In contrast to that’ a trapezoid is a four-sided figure with only one pair of parallel opposite sides, and it may or may not have a 90° angle in it. Also, opposite sides in a trapezoid need not be equal.
A rectangle is a quadrilateral with four right angles. The word rectangle is derived from the Latin word ‘rectangulus’, which can be split into ‘rectus’ meaning right and ‘angulus’ meaning angle. Opposite sides are parallel and equal, and the diagonals bisect each other and are also equal in a rectangle.
On the other hand, a trapezoid is a quadrilateral with a pair of parallel sides. The word trapezoid is derived from the Greek word ‘trapézion’, meaning a small table. A pair of opposite sides are parallel, and the diagonals intersect in a trapezoid.
Comparison Table Between Rectangle and Trapezoid
| Parameters of Comparison | Rectangle | Trapezoid |
| Definition | A rectangle is a four-sided parallelogram with four right angles and two pairs of parallel and equal opposite sides. | A trapezoid is a quadrilateral with a pair of parallel sides and a pair of intersecting diagonals. |
| Derivation of the word | The word ‘rectangle’ is derived from the Latin word ‘rectangulus’, which can be split into ‘rectus’ meaning right and ‘angulus’ meaning angle. | The word ‘trapezoid’ is derived from the Greek word ‘trapézion’, meaning a small table. |
| Parallelogram | A rectangle is a parallelogram since it has two pairs of parallel sides. | A trapezoid is not a parallelogram. |
| Opposite sides | The opposite sides of a rectangle are both parallel and equal in length. | A pair of opposite sides of a trapezoid are parallel. |
| Diagonals | Diagonals in a rectangle tend to be equal, and they bisect each other. | Diagonals in a trapezoid need not be equal, but they surely intersect each other. |
| Parallel sides | There are two parallel opposite sides in a rectangle. | There is only a pair of opposite parallel sides in a trapezoid. |
| 90° angles | There are four 90° angles in a rectangle. | There may or may not be 90° angles in a trapezoid. |
What is Rectangle?
A rectangle is a quadrilateral, i.e. a four-sided figure with two pairs of parallel and equal opposite sides. It contains four 90° angles. The word ‘rectangle’ is derived from the Latin word ‘rectangulus’, which can be split into ‘rectus’ meaning right and ‘angulus’ meaning angle.
It consists of two equal diagonals that bisect each other. You can draw a circle passing through all the four corners of a rectangle from the point of intersection of the diagonals. The sum of any two adjacent angles in a rectangle equals 180°, and the sum of all the angles in a rectangle equals 360°.
A square can be considered as a special type of rectangle with all the sides being equal. A rectangle is also a parallelogram since it has two pairs of parallel sides.
Main Differences Between Rectangle and Trapezoid
- A rectangle is a quadrilateral with four right angles, two equal opposite sides and two parallel opposite sides, whereas a trapezoid is a quadrilateral with just a pair of parallel opposite sides.
- The diagonals of a rectangle are equal, and they bisect each other, while the diagonals of a trapezoid aren’t equal, and they just intersect each other.
- The word rectangle is derived from the Latin word ‘rectangulus’, while the word trapezoid is derived from the Greek word ‘trapézion’.
- A rectangle is a parallelogram, while a trapezoid is not considered a parallelogram.
- There are two pairs of parallel sides in a rectangle, while there’s just a single pair of parallel sides in a trapezoid.
- In a broad sense, a rectangle can be considered a trapezoid, while a trapezoid can never be considered a rectangle.
Conclusion
There are so many quadrilaterals and parallelograms in mathematics, each with its specific characters and structures. Thus confusion between any two of them is quite obvious. Rectangle and trapezoid both are quadrilaterals, but between the two, only a rectangle is a parallelogram while a trapezoid isn’t.
A rectangle has two pairs of equal and opposite parallel sides, and it has four right angles, while a trapezoid has only a pair of opposite parallel sides. Diagonals bisect each other and are equal in a rectangle, while the diagonals only intersect each other in a parallelogram. They have significant differences in their structures.
References
- https://pubs.nctm.org/downloadpdf/journals/mt/107/7/article-p508.pdf
- https://www.jstor.org/stable/30024211