All six shapes are quadrilaterals, meaning they have four sides, but each shape has unique properties that distinguish them from each other. Let’s compare them in terms of similarities, differences, and their relations to one another.
1. Square:
- Definition: A quadrilateral with all sides equal and all angles equal to 90°.
- Properties:
- All sides are equal.
- All angles are 90°.
- Opposite sides are parallel.
- Diagonals bisect each other at 90° and are equal in length.
2. Rectangle:
- Definition: A quadrilateral with opposite sides equal and all angles equal to 90°.
- Properties:
- Opposite sides are equal and parallel.
- All angles are 90°.
- Diagonals are equal in length and bisect each other.
3. Rhombus:
- Definition: A quadrilateral where all sides are equal, but the angles are not necessarily 90°.
- Properties:
- All sides are equal.
- Opposite sides are parallel.
- Opposite angles are equal.
- Diagonals bisect each other at 90°, but diagonals are not equal.
4. Parallelogram:
- Definition: A quadrilateral with opposite sides that are equal and parallel.
- Properties:
- Opposite sides are equal and parallel.
- Opposite angles are equal.
- Diagonals bisect each other but do not form right angles.
5. Trapezium (Trapezoid):
- Definition: A quadrilateral with one pair of parallel sides.
- Properties:
- Only one pair of opposite sides is parallel.
- The other two sides (non-parallel sides) are called the “legs.”
- No restrictions on angles (they are not necessarily equal or 90°).
6. Kite:
- Definition: A quadrilateral with two pairs of adjacent sides equal.
- Properties:
- Two pairs of adjacent sides are equal.
- Diagonals intersect at right angles.
- One diagonal bisects the other.
Similarities:
| Shape | Similarities with Other Shapes |
|---|---|
| Square | – Square is a type of rectangle (equal angles, opposite sides parallel). – Square is also a rhombus (all sides equal). |
| Rectangle | – Rectangle is a type of parallelogram (opposite sides equal and parallel, diagonals bisect each other). |
| Rhombus | – Rhombus is a type of parallelogram (opposite sides are parallel, opposite angles are equal). |
| Parallelogram | – Both the rectangle and rhombus are specific types of parallelograms (different angle properties). |
| Trapezium | – Both the trapezium and other quadrilaterals have four sides (quadrilaterals). |
| Kite | – Kite and rhombus both have diagonals that intersect at 90°, but the properties of sides are different. |
Differences:
| Shapes | Differences |
|---|---|
| Square vs Rectangle | – Square has all sides equal, while in a rectangle only opposite sides are equal. – Diagonals of square bisect at 90°. |
| Square vs Rhombus | – Square has all angles equal to 90°, while in a rhombus angles are not 90°. – Diagonals of square are equal. |
| Square vs Parallelogram | – Square has all angles 90° and sides equal, while a parallelogram only has opposite sides equal and no right angles. |
| Rectangle vs Rhombus | – Rectangle has right angles, while in a rhombus the angles are not 90°. – Diagonals of rectangle are equal but not in a rhombus. |
| Rectangle vs Parallelogram | – Rectangle has right angles, but a parallelogram does not necessarily have right angles. |
| Rhombus vs Parallelogram | – In a rhombus, all sides are equal, while in a parallelogram, only opposite sides are equal. |
| Trapezium vs Parallelogram | – Trapezium has only one pair of parallel sides, while in a parallelogram, both pairs are parallel. |
| Trapezium vs Kite | – Trapezium has one pair of parallel sides, while a kite has no parallel sides. – Kite has two pairs of equal adjacent sides. |
| Kite vs Rhombus | – Kite has only adjacent sides equal, while in a rhombus all sides are equal. – Diagonals in a kite are unequal, while in a rhombus, diagonals are not necessarily equal but bisect at 90°. |
Detailed Comparison Table:
| Shape | Sides | Angles | Diagonals | Parallel Sides |
|---|---|---|---|---|
| Square | All sides equal | All angles 90° | Equal, bisect at 90° | Both pairs of opposite sides parallel. |
| Rectangle | Opposite sides equal | All angles 90° | Equal, bisect each other | Both pairs of opposite sides parallel. |
| Rhombus | All sides equal | Opposite angles equal | Bisect at 90°, but not equal | Both pairs of opposite sides parallel. |
| Parallelogram | Opposite sides equal | Opposite angles equal | Bisect each other, not at 90° | Both pairs of opposite sides parallel. |
| Trapezium | Only one pair of sides is parallel | No specific angle condition | Diagonals not necessarily equal or bisecting at 90° | Only one pair of sides is parallel. |
| Kite | Two pairs of adjacent sides equal | Only one pair of equal angles | Diagonals intersect at 90°, one bisects the other | No parallel sides. |
Concluding Relationships:
Square: A square can be considered both a rhombus (all sides equal) and a rectangle (all angles 90°). It is the most symmetrical quadrilateral.
Rectangle: A rectangle is a parallelogram with all angles equal to 90°. It shares properties with squares but differs in having only opposite sides equal.
Rhombus: A rhombus is a parallelogram with all sides equal, but the angles are not 90°. It shares properties with squares in terms of equal sides but differs in terms of angles.
Parallelogram: A parallelogram serves as the parent shape for squares, rectangles, and rhombuses. All these shapes have the property of having opposite sides that are equal and parallel.
Trapezium: A trapezium stands apart by having only one pair of parallel sides, making it less symmetrical than the other quadrilaterals.
Kite: A kite has two pairs of adjacent equal sides, which makes it distinct. Its diagonals intersect at right angles, similar to a rhombus, but only one diagonal bisects the other, unlike the diagonals in a rhombus or square.