Question

Explain how a square is a rectangle.

Answer 1

Hint: First we have to know a square is a two-dimensional plane figure with four equal sides, four interior right angles, and four corners. Then The similarities in the properties of a square and a rectangle can help us draw a conclusion to the question how a square is a rectangle.

Complete step-by-step answer:
In Geometry, we have learned about different types of shapes such as square, rectangle, cylinder, rhombus, cuboid, cube, cone, parallelogram, and so on. Many of these shapes share certain common properties. Square and rectangle are examples of such two-dimensional shapes. They both fall under the category of quadrilaterals.
 

A square is a quadrilateral or a \[4\]-sided polygon. All the angles are of equal measure. Therefore, it is considered as an equiangular quadrilateral. A rectangle is a two-dimensional figure with four sides, four interior right angles, and four corners. The opposite sides of a rectangle are equal. A rectangle has four angles, with each angle measuring \[{90^o}\]. Similar to a square, a rectangle is also referred to as an equiangular quadrilateral.
Let us have a look at the image given here to understand a square and a rectangle better.

Since both a square and a rectangle have an equal number of sides, we thus can conclude that both square and rectangle are quadrilaterals.
Properties of Square and Rectangle: In square all sides are equal but in rectangle, opposite sides are equal. In both rectangle and square opposite sides are parallel and all angles are equal. In both rectangle and square diagonals bisect each other. In square diagonals bisect perpendicularly but in rectangle diagonals are not bisect perpendicularly.
From the comparison drawn above for the common properties shared between a square and a rectangle, we observe that a square has all the properties that define a rectangle, which makes them alike in a certain manner. This means that a square can also be referred to as a type of rectangle. Hence, a square is a rectangle.

Note: Note that a square is a parallelogram with each angle a right angle. Also note that all squares are rectangles, but not all rectangles are squares. Also, all squares are rhombuses, but not all rhombuses are squares.