Question

Find counterexamples to disprove the statement. Statement: Every rectangle is a square.

Answer 1

Hint:By using the properties of rectangle and square we can disprove the above statement. We know the definition of square and rectangle. That is, in square all sides are equal while in rectangle opposite sides are equal. Let’s draw the diagram of squares and rectangles. By seeing the diagram we can identify the difference between them.

Complete answer:
Definition of square: A square is a closed two-dimensional plane figure with four sides. All the four sides of the square are of equal measure. Also, the four interior angles of a quadrilateral are of 90 degrees.

Definition of rectangle: A rectangle is a quadrilateral with four sides. The opposite side of a rectangle is parallel to each other. It means that the opposite sides of the rectangle are of equal measure. A rectangle has four angles, each measuring about 90 degrees.

See the above diagram, if we consider the rectangle length of AB as ‘a’ units and length of BC as ‘b’ the opposite sides will have the same length. While in square all the sides have the same length.
Here we see the counter examples or property in the table to disprove that every rectangle is a square (For above diagram).

Square	Rectangle
All sides are of equal length	Only the opposite sides are of equal length
Diagonals of a square are the perpendicular bisector of each other	Diagonals of a rectangle are not perpendicular bisector of each other
Area of square \[ = {a^2}\]	Area of Rectangle = \[ = a \times b\]
Perimeter of square \[ = 4 \times a\]	Perimeter of rectangle \[ = 2(a + b)\]

From above properties it is clear that a square has the same side length while a rectangle does not have the same side length. Hence it is concluded or proves that every rectangle is not a square.

Note: Similarities between rectangles and square: Squares and rectangles both are a type of quadrilateral, both have their four interior angles equal to 90 degrees and opposite sides parallel to each other. Knowing all the properties of triangle, rectangle, square, parallelogram, etc. it will help us to solve the problems based on them.