slide courtesy of miss fisher modified by mcconaughy 1/28/08 1 lesson 6.1 classifying quadrilaterals...
TRANSCRIPT
Slide Courtesy of Miss Fisher Modified by McConaughy 1/28/08
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LESSON 6.1
CLASSIFYING QUADRILATERALS
OBJECTIVE:To define and classify special types of quadrilaterals
Slide Courtesy of Miss Fisher Modified by McConaughy 1/28/08
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A ___________ is a four-sided polygon.
A ____ is a quadrilateral with two pairs of adjacent sides and no opposite sides .
NO PAIRS OF PARALLEL SIDES
quadrilateral
kite
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A __________ is a quadrilateral with exactly 1 pair of parallel sides.
An __________________ is a trapezoid whose nonparallel sides are .
1 PAIR OF PARALLEL SIDES
trapezoid
isosceles trapezoid
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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.
2 PAIRS OF PARALLEL SIDES
parallelogram
rhombus
rectangle
square
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Special Quadrilaterals
kites
True or false: A square is a rectangle and a rhombus. Explain.
Page Modified on 1/28/08
Slide Courtesy of Miss Fisher Modified by McConaughy 1/28/08
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Properties of Parallelograms: Angles
Use Same-Side Interior Angle Theorem to find the missing angles in the parallelogram below:
supplementary
120a
cb
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 _____________>
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Check for Understanding: Properties of Special Quadrilaterals
Parallelogram Rhombus Rectangle Square
Equilateral
Equiangular
Opp. Sides //
Opp. Sides =
Opp. Angles =
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EXAMPLE #1In parallelogram RSTU, mR = 2x – 10 and mS = 3x + 50. Find x.
U T
SR2x – 1
03x +
50
2x – 10 + 3x + 50 = 180
5x + 40 = 180
5x = 140x = 28
mR + mS = 180
RU || ST Def of Parallelogram
Substitution
Simplify
Subt prop of =
Div prop of =
SSI
Alert! Consecutive angles of a parallelogram are supplementary.
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EXAMPLE #2Find the values of the variables in the rhombus. Then find the lengths of the sides.
L N
TS
3b + 2
4b – 2
5a + 4 3a + 8
Find a.5a + 4 = 3a +
8 2a = 4a = 2Find
b.4b – 2 = 3b + 2 b =
4
LN =
3b + 2 =
3(4) + 2 =
14
ST =
4b – 2 =
4(4) – 2 =
14
LS =
5a + 4 =
5(2) + 4 =
14
NT =
3a + 8 =
3(2) + 8 =
14Alert! 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 #3Determine 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.
AB
CD
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EXAMPLE #3Determine 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.
Slope AB =Slope BC =
Slope CD =Slope DA =
4 – 32 – (-3) -1 – 4 3 – 2 -2 – (-
1) -2 – 3 3 – (-2)-3 – (-2)
15
15
-1-5
-5 1
= -5
5-1
= -5
=
=
=
=
= AB || CD and BC || DA b/c same slope
AB DA, AB BC, CD DA and CD BC b/c opposite reciprocal slopes
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EXAMPLE #3Determine 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 =
22 )34())3(2( 12522 )41()23(
22 ))1(2()32(
22 ))2(3())2(3(
=
=
=
=
125
125
125 =
=
=
= 26
26
26
26
All sides have the same length.The most precise name for the quad is a square.
Slide Courtesy of Miss Fisher Modified by McConaughy 1/28/08
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ASSIGNMENT
Pg 290 #1-13 (graph paper needed for #13), 20-24 even, 37-42