6'4 Rhombuses, Rectangles and Squares

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6.4 Rhombuses, Rectangles and Squares

• Pg 347

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Special Parallelograms

• Rhombus- a ogram with 4 _at_ sides
• Rectangle- a ogram with 4 rt ?s.
• Square- a ogram with 4 _at_ sides and 4 rt ?s

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So far (well add more later)
_
Quadrilaterals
_
parallelograms
_
_
rhombus
_
rectangle
square
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Examplesometimes, always, never

• A rhombus is a rectangle.
• Sometimes, if it is also a square
• A parallelogram is a rectangle.
• Sometimes, if is has 4 rt ?s
• A square is a rhombus.
• Always
• A rectangle is a square.
• Sometimes, if it has 4 _at_ sides

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Corollaries

• Rhombus corollary- a quad is a rhombus iff it
  has 4 _at_ sides.
• Rectangle corollary- a quad is a rectangle iff it
  has 4 rt ?s
• Square corollary- a quad is a square iff it is a
  rhombus and a rectangle.

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Thm 6.11

• A parallelogram is a rhombus iff its diagonals
  are ?.

J
K
If seg JL ? seg KM, then JKLM is a rhombus. If
JKLM is a rhombus, then seg JL ? seg KM
__
__
L
M
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Thm 6.12

• A ogram is a rhombus iff each diagonal bisects
  a pair of opposite ?s.

B
A
((
)
((
)
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))
(
(
D
C
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Thm 6.13

• A ogram is a rect? iff its diagonals are _at_.

Q
R
If QRST is a rectangle then seg QS _at_ seg RT
If seg QS ? seg RT then QRST is a rectangle.
T
S
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Assignment