### 8.4 Rhombuses Rectangles and Squares

```Warm Up
A Rhombus is…
• A parallelogram
• With all 4 sides
congruent.
A Rectangle is…
• A parallelogram with
• 4 right angles.
A Square is….
• A parallelogram
with…
• 4 congruent sides…
• And 4 congruent
angles.
Explore some of the properties
and attributes of Rhombuses,
Rectangles & Squares…
• Classzone.com for more examples
The diagram shows the
relationships between
parallelograms, rhombuses,
rectangles, and squares.
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•
•
•
•
All Parallelograms
All Rhombuses
All Rectangles
All Squares
Parallelograms
Rectangles
Rhombus
SQ
• Rhombus : A quadrilateral is a rhombus iff
it has four congruent sides.
• Rectangle: A quadrilateral is a rectangle iff
it has four right angles.
• Square: A quadrilateral is a square iff it is a
rhombus and a rectangle.
Theorems (p 349)
• Theorem 6.11: A parallelogram is a
rhombus iff its diagonals are
perpendicular.
• Theorem 6.12: A parallelogram is a
rhombus iff each diagonal bisects a pair of
opposite angles.
• Theorem 6.13: A parallelogram is a
rectangle iff its diagonals are congruent.
• A Rhombus is equilateral.
• The Diagonals of a rectangle are perpendicular.
• The opposite angles of a rhombus are
supplementary.
• A square is a rectangle.
• The diagonals of a rectangle bisect each other.
• The consecutive angles of a square are
supplementary.