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created by chris
markstrum © 2005
6.6 Specialized Quadrilaterals
California State Standards for Geometry
7: Prove & use theorems involving parallel lines and
properties of quadrilaterals.
8: Solve problems involving perimeter and area.
10: Compute area of polygons
12: Find and use measures of sides and angles of
triangles and polygons
quadrilateral relationships
Quadrilaterals
trapezoids
parallelograms
kites
squares
created by chris
markstrum 2005
created by chris
markstrum 2005
quadrilateral relationships
quadrilateral
kite
parallelogram
rhombus
rectangle
square
trapezoid
isosceles
trapezoid
Example
created by chris
markstrum 2005
A quadrilateral has at least one pair
of opposite sides congruent.
What kind of quadrilateral is it?
quadrilateral
kite
parallelogram
rhombus
rectangle
square
trapezoid
isosceles
trapezoid
Examples
created by chris
markstrum 2005
A quadrilateral has at least
two congruent consecutive sides.
What kind of quadrilateral is it?
quadrilateral
kite
parallelogram
rhombus
rectangle
square
trapezoid
isosceles
trapezoid
Example
created by chris
markstrum 2005
The coordinates of a quadrilateral are
(-2, 5), (1, 8), (4, 5), and (1, 2)
What kind of quadrilateral is it? Explain.
y
AB  BC  CD  AD  3 2
B
m AB  1
C
A
mBC  1
D
x
The quadrilateral
is a square
Example
created by chris
markstrum 2005
In quadrilateral RSTV,
mR  88, mS  113, mV  113
What kind of quadrilateral is it? Explain
quadrilateral
kite
parallelogram
rhombus
rectangle
square
trapezoid
isosceles
trapezoid
Example
created by chris
markstrum 2005
In quadrilateral RSTV,
mR  88, mS  113, mV  113
What kind of quadrilateral is it? Explain
S
R
kite
88o
S  V
113o
113o
V
 R and S
are not supplementary.
46o
T
created by chris
markstrum 2005
quadrilateral properties
Property
Both pairs of opp. sides //
X
X
X
X
sorry sorry
Exactly one pair of opp. sides are // sorry sorry sorry sorry sorry
Both pairs of opp. sides are 
X
X
X
X
sorry sorry
Exactly 1 pair of opp. sides are 
sorry sorry sorry sorry sorry
All sides are congruent
sorry sorry
X
X
X
sorry sorry
created by chris
markstrum 2005
quadrilateral properties
Property
X
X
X
sorry
X
sorry sorry
X
X
X
X
sorry sorry
X
X
X
X
sorry sorry
Diagonals are perpendicular
sorry sorry
Diagonals are congruent
sorry
Diagonals bisect each other
Both pairs of opp. angles are 
Exactly one pair of opp angles are  sorry sorry sorry sorry
All angles are congruent
sorry
X
sorry
X
X
X
sorry
sorry
sorry sorry
Summary


What characteristics must be considered
when classifying a quadrilateral?
Why must a parallelogram with one right
angle be a rectangle?
created by chris
markstrum 2005
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