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Chapter 6
Quadrilaterals
6.1 Classifying Quadrilaterals
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Parallelograms
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Rhombus
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Two pairs of adjacent sides congruent and no opposite sides congruent
Trapezoid
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Four congruent sides and four congruent angles
Kite
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Four right angles
Square
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Four congruent sides
Rectangle
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Both pairs of opposite sides are parallel
Exactly one pair of parallel sides
Isosceles Trapezoid
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Nonparallel sides are congruent
Classifying Quadrilaterals
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1. Is a square always a rectangle?
Classifying Quadrilaterals

2. Is a rectangle always a square?
Classifying Quadrilaterals

3. Is a square always a rhombus?
Classifying Quadrilaterals
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4. Is a rhombus always a square?
Classifying Quadrilaterals
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5. Is a square always parallelogram?
Classifying Quadrilaterals
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6. Is a kite always parallelogram?
Classifying Quadrilaterals
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7. Are there any shapes that are always
parallelograms?
Classifying Quadrilaterals
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Make a concept map
Include all quadrilaterals
–
Provide pictures, definitions, or key information
needed to link the quadrilaterals
Quadrilaterals
Parallelog
ram
Kite
Trapezoid
Rhombus
Rectangl
e
Isosceles
Trapezoid
Squar
e
Using properties of special
quadrilaterals
T
•Find the values of the
variables for the kite. Then
find the length of each side.
2y  5
x6
K
J
3x  5
2x  4
B
You try

Find the values of the variables.

x= _________,y=_____________
Assignment
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Worksheet and Pg 309 1-24
6.2 Properties of Parallelograms

What do you think the properties of a
parallelogram are? Sides? Angles?
Prove opposite sides of a
parallelogram are congruent


Given: ABCD is a Parallelogram
Prove: AB  CD, BC  DA
B
C
A
D
Properties of Parallelograms



6-1 Opposite sides of a parallelogram are
congruent.
6-2 Opposite angles of a parallelogram are
congruent
Consecutive angles of a parallelogram are
supplementary
Diagonals of a Parallelogram

Properties of parallelogram 6.2.gsp

Theorem 6-3
–
The diagonal of a parallelogram bisect each
other.
Theorem 6- 4
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If three or more parallel lines cut off
congruent segments on one transversal, then
they cut off congruent segments on every
transversal.
BD  DF
Assignment


H:\Geometry\lessons\Chapter 6.ppt
Pg 315, 1-41 odd
6.3 Proving that a Quadrilateral is a
Parallelogram



text book site
If both pairs of opposite sides of a
quadrilateral are congruent, then the
quadrilateral is a parallelogram.
If both pairs of opposite angles of a
quadrilateral are congruent then the
quadrilateral is a parallelogram.
More Theorems

If the diagonals of a quadrilateral bisect each
other, then the quadrilateral is a
parallelogram.

If one pair of opposites sides of a
quadrilateral is both congruent and parallel,
then the quadrilateral is a parallelogram.
Assignment

Pg 324, 1-10
6.4 Special Parallelograms
–


6-9 Each diagonal of a rhombus bisects two
angles of the rhombus.
6-10 The diagonals of a rhombus are
perpendicular.
–
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Properties of Rhombuses 6.4.gsp
Diagonals of a Rectangle 6.4.gsp
6-11 The diagonals of a rectangle are
congruent.
Is the parallelogram a rhombus or a
rectangle?
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6-12 If one diagonal of a parallelogram
bisects two angles of the parallelogram, then
the parallelogram is a rhombus.
6-13 If the diagonals of a parallelogram are
perpendicular, then the parallelogram is a
rhombus.
6-14 If the diagonals of a parallelogram are
congruent, then the parallelogram is a
rectangle.
Assignment

Pg 332, 1-17 odd 25-34 all
6.5 Trapezoids and Kites
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Trapezoids
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6-15 The base angles of an isosceles trapezoid
are congruent.
–
6-16 The diagonals of an isosceles trapezoid are
congruent.
Kites

6.5 Kite.gsp
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6-17 The diagonals of a kite are
perpendicular.
Assignment

Pg 338, 1-6 all, 8-16 even