Question

Explain how a square is a rectangle.

Answer 1

Hint: A rectangle is a polygon all of whose angles are equal to $ 90{}^\circ $ ("rect" means "right").
A square is a regular polygon of four sides, i.e. all four angles are equal and all four sides are also
equal.
Does a square satisfy the conditions of being a rectangle?

Complete step-by-step answer:
A rectangle, as the name suggests, is a four-sided polygon whose all angles are right angles, i.e. each
angle is equal to $ 90{}^\circ $ . It must, however, be noted that all sides of a rectangle need NOT
NECESSARILY be equal.
A square also has four sides and all angles equal. Since the sum of the inside angles of a four-sided
polygon (quadrilateral) is $ 180{}^\circ \times 4-360{}^\circ =720{}^\circ -360{}^\circ =360{}^\circ $ ,
every equal angle must be equal to $ \dfrac{360{}^\circ }{4}=90{}^\circ $ , or they must be right angles.

From the above discussion, we can conclude that a square is a rectangle because all its angles are right angles.

Note: A rectangle is a parallelogram but a parallelogram need not be a rectangle always.
Is a square a parallelogram?
A regular polygon has all angles equal and all sides "also" equal.
The sum of the exterior angles of any polygon is always $ 360{}^\circ $ .
The sum of the inside angles of an n-sided polygon is $ 180{}^\circ \times n-360{}^\circ $