Introduction:
A square is a special type of rectangle, but a rectangle is not a square. Although both shapes have similarities, they also have distinct characteristics that set them apart. Understanding the properties of each shape can help clarify why a square is considered a rectangle, but not vice versa.

Definition of a Square:
A square is a quadrilateral with four equal sides and four right angles. It possesses all the defining properties of a rectangle, making it a special case of a rectangle.

Definition of a Rectangle:
A rectangle is also a quadrilateral with four right angles, but unlike a square, its sides do not have to be equal in length. A rectangle can have two pairs of equal sides, but it is not required.

Key Differences:
1. Side Lengths: A square has all four sides of equal length, while a rectangle can have two pairs of equal sides or none at all. In a rectangle, the opposite sides are parallel and equal in length, but the adjacent sides may have different lengths.

2. Special Properties of a Square: A square possesses unique properties that differentiate it from a rectangle. Its diagonals are equal in length and bisect each other at right angles. In contrast, a rectangle's diagonals are equal in length but do not bisect each other at right angles unless it is a square.

3. Symmetry: A square has rotational symmetry of 90 degrees, meaning it looks the same after a quarter turn. A rectangle, on the other hand, has rotational symmetry of 180 degrees, requiring a half turn to look the same.

Why a Square is a Rectangle:
A square is considered a rectangle because it meets the definition of a rectangle. A rectangle is defined as a quadrilateral with four right angles, and a square fulfills this requirement. Additionally, a square has parallel sides, opposite sides of equal length, and diagonals that bisect each other at right angles, just like a rectangle. Therefore, a square can be classified as a special case of a rectangle.

Why a Rectangle is not a Square:
Although a square is a rectangle, a rectangle is not a square because it does not possess all the defining properties of a square. A rectangle can have sides of different lengths, which is not the case for a square. Additionally, a rectangle's diagonals do not bisect each other at right angles unless it is a square. Therefore, while a rectangle shares some similarities with a square, it lacks the specific properties that make a square distinct.