Square vs Rhombus: Analyzing Properties of Quadrilaterals in Geometry

To determine whether a rhombus is a square, we must understand the properties of each shape.

Definition of a Rhombus:
A rhombus is a quadrilateral with all four sides of equal length. It may have angles that are not right angles.

Definition of a Square:
A square is a quadrilateral with all four sides of equal length and all four angles equal to $90^{\circ}$.

Comparison:

• Both a square and a rhombus have four equal sides.
• A square has $90^{\circ}$ angles, whereas a rhombus does not necessarily have $90^{\circ}$ angles.

Thus, while all squares are rhombuses (because they have equal side lengths), not all rhombuses are squares (because not all rhombuses have right angles).

Therefore, a rhombus is not a square as a general statement.