1. 6-4 Properties of Rhombuses, Rectangles, and Squares

2. Rectangles Definition:
A quadrilateral with four right angles. (this is all we know)
What condition does this satisfy to be classified a parallelogram?

3. Properties of a Rectangle
-Opposite sides are congruent
-Opposite sides are parallel
-Opposite angles are congruent
-Diagonals bisect each other
-Consecutive angles supplementary
-Interior angles sum to 360
Why are these 6 properties true for a rectangle?
-The diagonals of a rectangle are congruent.
Theorem

4. Label everything we know about this figure.

5. Rhombus
Definition:
A quadrilateral with four congruent sides. (all we know)
What allows us to classify this as a parallelogram?

6. Properties of a Rhombus
-Opposite sides are congruent
-Opposite sides are parallel
-Opposite angles are congruent
-Diagonals bisect each other
-Consecutive angles supplementary
-Interior angles sum to 360
Why are these 6 properties true for a rhombus?
The diagonals of a rhombus are perpendicular.
Each diagonal of a rhombus bisects 2 angles of the rhombus
Theorem
Theorem

7. Label everything we know about this figure.

8. Square
Definition:
A quadrilateral with four right angles and four congruent sides.

9. Properties of a square -Opposite sides are congruent
-Opposite sides are parallel
-Opposite angles are congruent
-Diagonals bisect each other
-Consecutive angles supplementary
-Interior angles sum to 360
Is a square a rectangle? Why or why not?
Is a square a rhombus? Why or why not?
Do we then know that a square also shares the properties of those 2 figures?

10. Label everything that we know about this square

11. (If I were to place the first figure in front of you, would it also be the second figure) Is a rectangle a square? Is a rhombus a square?

12. Theorem
If an angle of a parallelogram is a right angle, then the parallelogram is a rectangle.
(what would we need to know for it to be a square)
If 2 consecutive sides of a parallelogram are congruent, then the parallelogram is a rhombus.
Theorem

13. Quadrilateral Flow Chart
Polygons
Quadrilateral
Parallelogram
Kite
Square
Rectangle
Rhombus
Trapezoid