Square

Definition

A square is a special type of quadrilateral that has four equal sides and four right angles. It is a unique shape because it possesses the properties of both a rectangle and a rhombus, making it a versatile figure in geometry. Squares play a significant role in understanding the broader classification of quadrilaterals, parallelograms, symmetry, and special types of quadrilaterals.

5 Must Know Facts For Your Next Test

1. A square is classified as both a rectangle and a rhombus, meaning it inherits their properties such as having opposite sides parallel and all sides equal.
2. The diagonals of a square are equal in length, bisect each other at right angles, and also bisect the angles of the square.
3. All squares are also parallelograms, which means they have pairs of opposite sides that are parallel and equal in length.
4. The area of a square can be calculated using the formula: Area = side × side or Area = side².
5. The perimeter of a square is calculated as Perimeter = 4 × side length.

Review Questions

• How does the classification of a square fit into the broader category of quadrilaterals, and what unique properties does it possess?
  • A square fits into the category of quadrilaterals as it has four sides. What makes it unique is that it has both four equal sides and four right angles, distinguishing it from other quadrilaterals. Additionally, as a specific type of parallelogram, it shares properties like having opposite sides that are parallel and congruent. This combination of features allows it to inherit characteristics from both rectangles and rhombuses.
• In what ways do the properties of a square influence its classification as a special type of parallelogram?
  • The properties of a square heavily influence its classification as a special type of parallelogram due to its characteristics. Specifically, all squares have parallel opposite sides and congruent angles. Furthermore, since all sides are equal in length and all angles are right angles, a square meets all criteria for being classified as both a rectangle (due to its right angles) and a rhombus (due to its equal sides). This unique combination solidifies its status as a special case among parallelograms.
• Evaluate how the symmetrical properties of squares contribute to their significance in both two-dimensional and three-dimensional geometry.
  • Squares possess symmetrical properties that make them highly significant in geometry, both in two dimensions and three dimensions. In two dimensions, squares exhibit four lines of symmetry and rotational symmetry at 90-degree intervals, allowing for consistent patterns in design and tiling. In three-dimensional geometry, when squares are used to form structures like cubes, they contribute to symmetrical features that are essential for balance and aesthetics. The uniformity and predictability derived from these symmetrical attributes make squares an essential concept in geometric studies.

Related terms

Quadrilateral:

A polygon with four sides and four vertices.

Rectangle: A parallelogram with four right angles and opposite sides that are equal in length.

Rhombus:

A parallelogram with all four sides of equal length but not necessarily with right angles.