Square and rectangle are both quadrilaterals ( as they have 4 sides). Every square is a rectangle. Though all quadrilaterals have four sides and the sum of angles equals 360o, but only squares and rectangles have all the angles equal to 90o. The difference is with respect to the lengths of the sides. In a square, all four sides are equal. In this article, we prove that every square is a rectangle but every rectangle is not a square.
Every square is a rectangle?
Similarities between a rectangle and square
- Both squares and rectangles are quadrilaterals.
- Both squares and rectangles have all angles equal to 90o.
- The opposites are equal and parallel in both squares and rectangles
Why is a square a type of rectangle?
Properties of a rectangle:
- Opposite sides should be equal and parallel
- All angles should be equal to 90o
- Diagonals bisect each other and are equal
Both these properties are true for a square, the opposite sides are equal, the diagonals bisect each other, and are equal plus all angles are equal to 90o. Hence, every square is a rectangle.
In the above image, we can see that in a rectangle, when a=b (that is, the length of the rectangle is equal to the breadth of the rectangle), we get a square). That means every square is a type of rectangle in which a=b. The same is not true the other way around.
Why is every rectangle not a type of square?
Properties of a square:
- All sides should be equal
- All angles should be equal to 90o
- Diagonals bisect each other and are equal
Though all angles are equal to 90o in a rectangle and diagonals bisect each other and are equal, but all sides are not equal. Hence every rectangle is not a square.
Hence, we can consider a square as a special type of rectangle that has all sides equal. This example can be thought to relate easier ” all mobile phones are electronic gadgets, but all electronic gadgets are not mobile phones”. So, all squares are rectangles but all rectangles are not squares.
Is the rhombus a type of rectangle?
Rhombus is a quadrilateral that has all sides equal, opposite sides are parallel, the sum of opposite angles is 180, and the diagonals bisect each other. Rectangle satisfies all the conditions except for all equal sides. Hence, a rectangle is not a type of rhombus. On the other hand, a square has all sides equal, with opposite sides parallel, the sum of opposite sides is 180, and the diagonals bisect each other. Hence, every square is a rhombus.
