6-4%20Properties%20of%20Rhombuses,%20Rectangles,%20and%20Squares

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6-4 Properties of Rhombuses, Rectangles, and
Squares

• -rectangle
• -rhombus
• -square

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Rectangles
Definition A quadrilateral with four right
angles. (this is all we know) What condition
does this satisfy to be classified a
parallelogram?
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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
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Label everything we know about this figure.
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Rhombus
Definition A quadrilateral with four congruent
sides. (all we know) What allows us to classify
this as a parallelogram?
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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
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Label everything we know about this figure.
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Square
Definition A quadrilateral with four right
angles and four congruent sides.
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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?
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Label everything that we know about this square
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(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?
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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
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Quadrilateral Flow Chart
Polygons
Quadrilateral
Parallelogram
Kite
Square
Rectangle
Rhombus
Trapezoid
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