5
Transcript of 5
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Special Quadrilaterals6.6
Chapter 6Section 6.6
Special Quadrilaterals
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Special Quadrilaterals6.6
Kite
Square
Trapezoid
Rhombus
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Special Quadrilaterals6.6
IDENTIFY SPECIAL QUADRILATERALS
X X X X
X
X
X X X
X X X X
X
X
X X
X
X X X
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Special Quadrilaterals6.6
IDENTIFY SPECIAL QUADRILATERALS
One pair of opposite sides ||
One Pair of Opposite sides
Isosceles Trapezoid
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Special Quadrilaterals6.6
IDENTIFY SPECIAL QUADRILATERALS
Both Pairs of opposite angles
Parallelogram, Rectangle, Rhombus, Square
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Special Quadrilaterals6.6
IDENTIFY SPECIAL QUADRILATERALS
Diagonals bisect each other
Parallelogram, Rectangle, Rhombus, Square
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Special Quadrilaterals6.6
IDENTIFY SPECIAL QUADRILATERALS
65
ABCD is a parallelogram
A parallelogram with adjacent sides is a Rhombus
BCAB
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Special Quadrilaterals6.6
IDENTIFY SPECIAL QUADRILATERALS
ABCD is a trapezoid
Trapezoid with legs is isosceles
BCAD
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Special Quadrilaterals6.6
IDENTIFY SPECIAL QUADRILATERALS
Need 4 Right angles and 4 Sides
A Rhombus with 1 right angle is a square
DCABBCAD
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Special Quadrilaterals6.6
PROVE A QUADRIALTERAL IS A SPECIAL TYPE
P(5, 4)
Q(3, -6)
R(0, -10)
S(2, 0)
Looks like a parallelogram
Find the slope of each side and show that opposite sides are parallel
Clearly not all sides are
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Special Quadrilaterals6.6
PROVE A QUADRIALTERAL IS A SPECIAL TYPE
P(5, 4)
Q(3, -6)
R(0, -10)
S(2, 0)
35)6(4
MPQ
210 5
02)10(0
MSR
210 5
SR||PQ
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Special Quadrilaterals6.6
PROVE A QUADRIALTERAL IS A SPECIAL TYPE
P(5, 4)
Q(3, -6)
R(0, -10)
S(2, 0)
2504
MPS
34
03)10(6
MQR
34
SR||PQ
QR||PS
PQRS is a parallelogram
Definition of Parallelogram
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Special Quadrilaterals6.6
PROVE A QUADRIALTERAL IS A SPECIAL TYPE
P(4, 8)Q(0, 9)
R(-2, 1) S(2, 0)
Looks like a rectangle
Show 4 right angles
Find slopes and show that they are negative reciprocals
Clearly it is not a Rhombus
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Special Quadrilaterals6.6
PROVE A QUADRIALTERAL IS A SPECIAL TYPE
P(4, 8)Q(0, 9)
R(-2, 1) S(2, 0)
2408
MPS 4
28
4089
MPQ
41
)2(019
MQR 4
28
2221
MSR
41
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Special Quadrilaterals6.6
PROVE A QUADRIALTERAL IS A SPECIAL TYPE
P(4, 8)Q(0, 9)
R(-2, 1) S(2, 0)
QPPS
RSPS
QPQR
RSQR
PQRS is a rectangle
A Quadrilateral with 4 right angles is a rectangle
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Special Quadrilaterals6.6
PROVE A QUADRIALTERAL IS A SPECIAL TYPE
Looks like a Rhombus
Show all sides congruent
Find length of each side and show that they are the same
Clearly it is not a Rectangle
2 22 1 2 1( ) ( )d x x y y
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Special Quadrilaterals6.6
PROVE A QUADRIALTERAL IS A SPECIAL TYPE
2 2(15 8) (5 4)RS 2 2(7) (1)RS
2 2(8 1) (4 5)PS 2 2(7) ( 1)PS
50 5 2RS
50 5 2PS
2 2(8 1) (6 5)PQ 2 2(7) (1)PQ
50 5 2PQ
2 2(15 8) (5 6)QR 2 2(7) ( 1)QR
50 5 2QR
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Special Quadrilaterals6.6
PROVE A QUADRIALTERAL IS A SPECIAL TYPE
PQ QR RS PS
PQRS is a Rhombus
A Quadrilateral with 4 congruent sides is a rhombus
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Special Quadrilaterals6.6
PROVE A QUADRIALTERAL IS A SPECIAL TYPE
PQRS is a Rectangle
A Quadrilateral with 4 right angles is a rectangle
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Special Quadrilaterals6.6
HW #74Pg 367-370 8-36, 38, 40, 45-50,
53, 56-64 Even