List the differences between a square and a rhombus.

Here are the key differences between a square and a rhombus:

Definition: A square is a quadrilateral (a four-sided polygon) with four equal sides and four right angles. A rhombus is also a quadrilateral with four equal sides, but its angles are not necessarily right angles.

Angle properties: In a square, all four angles are right angles, measuring 90 degrees each. In a rhombus, the angles can be acute (less than 90 degrees), obtuse (greater than 90 degrees), or right angles.

Side lengths: All sides of a square are equal in length. In a rhombus, all four sides are also equal in length.

Diagonals: The diagonals of a square are equal in length and bisect each other at right angles. In a rhombus, the diagonals are equal in length but do not necessarily intersect at right angles.

Symmetry: A square has four lines of symmetry. It can be folded along these lines to create congruent halves. A rhombus also has four lines of symmetry but does not have congruent halves when folded along these lines.

Tiling properties: Squares can tile a plane without leaving any gaps or overlaps. Rhombuses can also tile a plane, but they leave gaps between the shapes.

Special cases: A square can be considered as a special type of rhombus where all angles are right angles. On the other hand, a rhombus can be considered as a special type of parallelogram (a quadrilateral with opposite sides parallel) where all sides are equal.

It's important to note that while a square is a specific type of rhombus, not all rhombuses are squares.