This document defines and compares properties of rhombuses, rectangles, and squares. A rhombus is a parallelogram with 4 congruent sides and perpendicular diagonals. A rectangle is a parallelogram with 4 right angles and congruent diagonals. A square has the combined properties of a rhombus, rectangle, and parallelogram - it is a rhombus and rectangle with 4 equal sides and right angles.

1. Terms of Endearment
Rhombi, Rectangles, and Squares: 6.4

2. Rhombus
• Parallelogram with 4 congruent
sides
• The two diagonals are perpendicular
to each other
• The two diagonals bisect the
opposite angles

3. Rectangle
• Parallelogram with 4 right angles
• The two diagonals are congruent

4. Square
• Parallelogram with 4 congruent
angles and 4 right angles
• The square adds no new
characteristics, it is the combination
of all the characteristics of a
quadrilateral, parallelogram,
rectangle and rhombus

5. Corollaries
• A quadrilateral is a rhombus if and
only if it has 4 congruent sides
• A quadrilateral is a rectangle if and
only if it has four right angles
• A quadrilateral is a square if and
only if it is a rhombus and a
rectangle

6. Quadrilateral Relationships:
Quadrilateral
Parallelogram
Rectangle Rhombus
Square