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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

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Page 1: Created by chris markstrum © 2005 6.6 Specialized Quadrilaterals California State Standards for Geometry 7: Prove & use theorems involving parallel lines

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

Page 2: Created by chris markstrum © 2005 6.6 Specialized Quadrilaterals California State Standards for Geometry 7: Prove & use theorems involving parallel lines

created by chris markstrum 2005

quadrilateral relationshipsQuadrilaterals

parallelograms

rectangles rhombi

squaressquares

trapezoids

kites

Page 3: Created by chris markstrum © 2005 6.6 Specialized Quadrilaterals California State Standards for Geometry 7: Prove & use theorems involving parallel lines

created by chris markstrum 2005

quadrilateral relationships

quadrilateral

kite parallelogram

trapezoid

rhombus rectangle

square

isosceles trapezoid

Page 4: Created by chris markstrum © 2005 6.6 Specialized Quadrilaterals California State Standards for Geometry 7: Prove & use theorems involving parallel lines

created by chris markstrum 2005

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

Page 5: Created by chris markstrum © 2005 6.6 Specialized Quadrilaterals California State Standards for Geometry 7: Prove & use theorems involving parallel lines

created by chris markstrum 2005

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

Page 6: Created by chris markstrum © 2005 6.6 Specialized Quadrilaterals California State Standards for Geometry 7: Prove & use theorems involving parallel lines

created by chris markstrum 2005

Property

sorry

only

isosceles

X XXX

X

X X X X

X X

sorry

sorry

sorry

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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

Page 7: Created by chris markstrum © 2005 6.6 Specialized Quadrilaterals California State Standards for Geometry 7: Prove & use theorems involving parallel lines

created by chris markstrum 2005

Property

sorry

sorry

X

X X

X X X

X

X

X

X X

X X XX

X

sorry

sorry

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sorry

sorry

sorry

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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

Page 8: Created by chris markstrum © 2005 6.6 Specialized Quadrilaterals California State Standards for Geometry 7: Prove & use theorems involving parallel lines

created by chris markstrum 2005

Summary What characteristics must be

considered when classifying a quadrilateral?

Why must a parallelogram with one right angle be a rectangle?


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