Question

Why is a square a parallelogram?

Answer 1

A square has all the properties of a parallelogram and can therefore be considered to be a parallelogram

Explanation:

The properties of a parallelogram can be stated according to:

the sides

the angles

the diagonals

the symmetry

A parallelogram has:

$2$ pairs of opposite sides parallel

$2$ pairs of opposite sides equal

The sum of the angles is ${360}^{\circ }$

$2$ pairs of opposite angles are equal

The diagonals bisect each other

It has rotational symmetry of order $2$

All of these properties apply to square, so it can be considered to be a parallelogram.

However a square has additional properties as well, so it can be regarded as a special type of parallelogram.

A square has:

$2$ pairs of opposite sides parallel

All its sides equal

The sum of the angles is ${360}^{\circ }$

All its angles are equal (to ${90}^{\circ }$)

The diagonals bisect each other at ${90}^{\circ }$

The diagonals are equal.

The diagonals bisect the angles at the vertices to give ${45}^{\circ }$angles.

$4$ lines of symmetry

It has rotational symmetry of order $4$