Understanding the Key Differences Between a Square and a Rhombus
When it comes to geometry, two shapes that are often confused with each other are the square and the rhombus. At first glance, both shapes appear to be very similar since they both have four sides and look like squares. However, there are some key differences between them that set them apart.
Definition of a Square
A square is a four-sided polygon where all sides are equal in length and all angles are right angles (90 degrees). It can be considered a special type of rectangle, but with all sides of equal length. In other words, every square is a rectangle, but not every rectangle is a square.
Definition of a Rhombus
A rhombus is also a four-sided polygon but the sides are not necessarily of equal length. The defining feature of a rhombus is that all four sides are of the same length. Moreover, the opposite angles in a rhombus are congruent, but they are not necessarily right angles.
Difference in Shape
The most noticeable difference between a square and a rhombus is the shape. A square has four sides of equal length with right angles at each of the four corners. That is, all four corners are 90° angles. In contrast, a rhombus has four sides of equal length, but its corners are not right angles. Instead, its sides meet to form acute angles.
Difference in Area
While a square and a rhombus may have four sides of equal length, their areas are not necessarily equal. A square has the maximum area of any quadrilateral with the same perimeter, whereas a rhombus has an area that is slightly smaller. This is because, in a square, the area is maximized when all sides are different. In a rhombus, however, the area is maximized when the angles are acute.
Difference in Diagonal Lengths
Another notable difference between a square and a rhombus is the length of their diagonal. Since all sides of a square are equal, the diagonal of a square is also equal in length to its sides. In a rhombus, on the other hand, the two diagonals are not of equal length. The longer diagonal divides the rhombus into two congruent triangles.
Conclusion
In conclusion, the square and the rhombus are two shapes that may look similar but are different in several ways. A square has four sides of equal length with right angles at each corner, while a rhombus has four sides of equal length but with acute angles at each corner. They also have different areas and diagonal lengths. By understanding these differences, you can easily identify the difference between a square and a rhombus.
Table difference between a square and a rhombus
| Square | Rhombus | |
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| Definition | A square is a quadrilateral with all sides equal in length and all angles equal to 90 degrees. | A rhombus is a quadrilateral with all sides equal in length and opposite angles equal to each other. |
| Properties |
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| Shape | A square has four equal sides and four right angles. Its shape is therefore a rectangle with all sides equal. | A rhombus has four equal sides and opposite angles that are equal. Its shape is usually represented as a leaning square. |
| Examples |
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