What shapes are rectangles and squares

A rectangle, a mathematical term for a parallelogram that has one angle that is a right angle is called a rectangle. It is also defined as a parallelogram in which all four angles are right angles.

A square is a quadrilateral with all four sides equal and all four angles at right angles.

The properties of a rectangle are: two diagonals are equal; two diagonals are bisecting each other; two sets of opposite sides are parallel; two sets of opposite sides are equal; four angles are right angles; there are two axes of symmetry (a square has four); it is unstable (easily deformable); the square of a rectangle's diagonal length is the sum of the square of the lengths of the sides; and the quadrilateral obtained by joining the midpoints of each of the sides of a rectangle in turn is a rhombus.

The properties of a square are: each set of opposite sides of a square is parallel and all four sides are equal; all four angles are 90°; the diagonals are perpendicular, bisecting, and equal to each other, and each diagonal bisects a set of opposite angles.

Extended information:

Area of a rectangle formula

Area of a rectangle = length x width

Perimeter of a rectangle formula

Rectangle perimeter = (length + width) x 2

Square Determination Theorem:

1: A rhombus with equal diagonals is a square.

2: A rhombus with one right angle is a square.

3: A rectangle with diagonals perpendicular to each other is a square.

4: A rectangle with a set of equal neighboring sides is a square.

5: A set of parallelograms with equal neighboring sides and one angle is a right angle is a square.

6: A parallelogram whose diagonals are perpendicular to each other and equal is a square.