CLASSIFYING QUADRILATERALS

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LESSON 6.1 CLASSIFYING QUADRILATERALS
OBJECTIVE To define and classify special types
of quadrilaterals
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NO PAIRS OF PARALLEL SIDES
quadrilateral
A ___________ is a four-sided polygon. A ____
is a quadrilateral with two pairs of adjacent
sides ? and no opposite sides ?.
kite
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1 PAIR OF PARALLEL SIDES
trapezoid
A __________ is a quadrilateral with exactly 1
pair of parallel sides. An __________________
is a trapezoid whose nonparallel sides are ?.
isosceles trapezoid
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2 PAIRS OF PARALLEL SIDES
parallelogram
A _____________ is a quadrilateral with both
pairs of opposite sides parallel. A _________
is an equilateral parallelogram. A _________ is
an equiangular parallelogram. A _______ is an
equilateral and equiangular parallelogram.
rhombus
rectangle
square
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Special Quadrilaterals
Page Modified on 1/28/08
True or false A square is a rectangle and a
rhombus. Explain.
kites
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Properties of Parallelograms Angles

• Use Same-Side Interior Angle Theorem to find
  the missing angles in the parallelogram below

a
b
120
c
supplementary
The consecutive angles in a are
_____________. The opposite angles in a
are _____________.
congruent
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Check for Understanding Summary Properties of
Parallelograms

• Opposite sides are _________________. (DEF.)
• Opposite sides are _________________.
• Opposite angles are ________________.
• Consecutive angles are _____________gt

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Check for Understanding Properties of Special
Quadrilaterals
Parallelogram Rhombus Rectangle Square
Equilateral Equilateral
Equiangular Equiangular
Opp. Sides // Opp. Sides //
Opp. Sides Opp. Sides
Opp. Angles Opp. Angles
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EXAMPLE 1
U
T
In parallelogram RSTU, m?R 2x 10 and m?S 3x
50. Find x.
2x 10
3x 50
R
S
Def of Parallelogram
RU ST
SSI
m?R m?S 180
Substitution
2x 10 3x 50 180
Simplify
5x 40 180
Subt prop of
5x 140
Alert! Consecutive angles of a parallelogram are
supplementary.
Div prop of
x 28
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EXAMPLE 2
3b 2
N
L
Find the values of the variables in the rhombus.
Then find the lengths of the sides.
5a 4
3a 8
S
T
4b 2
Find a.
LN
3b 2
3(4) 2
14
5a 4 3a 8
2a 4
ST
4b 2
4(4) 2
14
a 2
Find b.
LS
5a 4
5(2) 4
14
4b 2 3b 2
b 4
NT
3a 8
3(2) 8
14
Alert! Opposite sides of a parallelogram are
congruent.
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Classifying Quadrilaterals

• During this lesson, you will classify
  quadrilaterals algebraically by using Distance
  Formula and Slope Formula.

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Algebra Review

• Two lines which have the same slope are
  _____________ to each other.
• Two lines whose slopes are negative (opposite)
  reciprocals are ___________________ to each
  other.
• Given two points (x1, y1) and (x2, y2),
  write
• Slope Formula ____________________
• Distance Formula__________________

parallel
perpendicular
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EXAMPLE 3
Determine the most precise name for the
quadrilateral with vertices A(-3,3), B(2,4),
C(3,-1) and D(-2,-2).
1. Graph quadrilateral ABCD.
B
A
C
D
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EXAMPLE 3
Determine the most precise name for the
quadrilateral with vertices A(-3,3), B(2,4),
C(3,-1) and D(-2,-2). Explain your response.
2. Find the slope of each side.
4 3 2 (-3)
1 5
Slope AB

AB CD and BC DA b/c same slope
-1 4 3 2
-5 1
Slope BC

-5
AB ? DA, AB ? BC, CD ? DA and CD ? BC b/c
opposite reciprocal slopes
-2 (-1) -2 3
1 5
-1 -5


Slope CD
3 (-2) -3 (-2)
5 -1
Slope DA

-5
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EXAMPLE 3
Determine the most precise name for the
quadrilateral with vertices A(-3,3), B(2,4),
C(3,-1) and D(-2,-2).
2. Find the length of each side.

AB

BC


CD


DA


All sides have the same length.
The most precise name for the quad is a square.
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ASSIGNMENT
Pg 290 1-13 (graph paper needed for 13),
20-24 even, 37-42