Rhombi and Squares

Rhombus

A rhombus is a parallelogram with four congruent sides.

Special Properties:

• All sides are congruent.
• Diagonals are perpendicular.
• Each diagonal bisects a pair of opposite angles.
• Diagonals bisect each other (parallelogram property).

Square

A square is a parallelogram that is both a rectangle and a rhombus. It has all the properties of both:

• Four congruent sides (rhombus).
• Four right angles (rectangle).
• Diagonals are congruent (rectangle), perpendicular (rhombus), and bisect each other and the angles.

Quadrilateral Hierarchy

Parallelogram → Rectangle (right angles), Rhombus (equal sides) → Square (both)