Any shape that has four sides at right angles to each other with diagonals of equal length is a rectangle. The two special types of rectangles are squares and Fibonacci rectangles.

Shapes are classified based on the criteria that they meet. They range from the basic shapes like polygons, which have only a few criteria to meet, to shapes that have more specific criteria, such as rectangles. Polygons are closed shapes that have multiple sides. Any polygon that has four sides is a quadrilateral. Parallelograms are special quadrilaterals whose opposite sides are of equal length. Rectangles are a special kind of parallelogram where not only are the opposite sides of equal length, but the diagonals are also of equal length. The sides are at right angles to each other. Any shape that satisfies these three criteria qualifies as a rectangle.

A square is considered to be a special kind of rectangle because it has diagonals of equal length and sides that are at right angles to each other. Instead of having a long side and a short side, a square has four sides of equal length.

A Fibonacci rectangle has a length-to-width ratio of 1.618-to-1. Because it follows the golden ratio, a Fibonacci rectangle is also called the golden rectangle.