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 polygons12: Find and use measures of sides and angles of triangles and polygons
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quadrilateral relationshipsQuadrilaterals
parallelograms
rectangles rhombi
squaressquares
trapezoids
kites
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quadrilateral relationships
quadrilateral
kite parallelogram
trapezoid
rhombus rectangle
square
isosceles trapezoid
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B
C
D
A
ExampleThe coordinates of a quadrilateral are (-2, 5), (1, 8), (4, 5), and (1, 2)What kind of quadrilateral is it? Explain.
x
y 3 2AB BC CD AD
ABm
The quadrilateral is
a squareBCm
1
1
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Example
In quadrilateral RSTV,
What kind of quadrilateral is it? Explain88 , 113 , 113m R m S m V
parallelogram
rhombus rectangle
square
trapezoid
isosceles
trapezoid
kite
quadrilateral
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Property
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only
isosceles
X XXX
X
X X X X
X X
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Both pairs of opp. sides //
Exactly one pair of opp. sides are //
Both pairs of opp. sides are
Exactly 1 pair of opp. sides are
All sides are congruent
quadrilateral properties
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Property
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X
X X
X X X
X
X
X
X X
X X XX
X
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Diagonals are perpendicular
Diagonals are congruent
Diagonals bisect each other
Both pairs of opp. angles are
Exactly one pair of opp angles are
All angles are congruent
quadrilateral properties
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Summary What characteristics must be
considered when classifying a quadrilateral?
Why must a parallelogram with one right angle be a rectangle?