Transcript 6.5 Rhombi and Squares - Ms. Fowls' Math Classes

6.5 Rhombi and Squares
Rhombus
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Quad with 4  sides
Rhombus
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Theorem 6.15: The diagonals
of a rhombus are  .
Theorem 6.16: If the
diagonals of a parallelogram
are , then the parallelogram
is a rhombus.
Theorem 6.17: Each
diagonal of a rhombus bisects
a pair of opposite angles.
All 4 of the s are .
Example
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Refer to Example #2 picture on page 349
Do Check Your Progress #2
Answer:
114
Square
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Both a rhombus and a rectangle
All sides are 
All angles are right angles (90°)
Quadrilaterals
Parallelograms
Rhombi
Squares
Rectangles
Example
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Given the vertices J(5,0), K(8, -11), L (-3,-14), M(6,-3), determine whether parallelogram JKLM is a
rhombus, a rectangle, or a square. List all that apply.
Use the distance formula to compare the lengths of
the diagonals. Use the slope formula to determine if
the sides are perpendicular.
Answer: Square, rectangle, and rhombus, all sides
are congruent and perpendicular.
Summaries
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Rhombus Properties
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Opposites sides are 
Opposite angles are 
Consecutive angles are
supplementary.
Diagonals bisect each other
Diagonals are perpendicular
Each diagonal bisects two angles.
4 sides are 
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Square Properties
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Opposites sides are 
Opposite angles are 
Consecutive angles are
supplementary.
Diagonals bisect each other
Diagonals are perpendicular
Each diagonal bisects two angles.
All four angles are right angles.
Diagonals are 
4 sides are 
Homework #40
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p. 352 11, 15-18, 19-25 odd, 31-34