Post on 28-May-2015
Special Quadrilaterals6.6
Chapter 6Section 6.6
Special Quadrilaterals
Special Quadrilaterals6.6
Kite
Square
Trapezoid
Rhombus
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
Special Quadrilaterals6.6
IDENTIFY SPECIAL QUADRILATERALS
One pair of opposite sides ||
One Pair of Opposite sides
Isosceles Trapezoid
Special Quadrilaterals6.6
IDENTIFY SPECIAL QUADRILATERALS
Both Pairs of opposite angles
Parallelogram, Rectangle, Rhombus, Square
Special Quadrilaterals6.6
IDENTIFY SPECIAL QUADRILATERALS
Diagonals bisect each other
Parallelogram, Rectangle, Rhombus, Square
Special Quadrilaterals6.6
IDENTIFY SPECIAL QUADRILATERALS
65
ABCD is a parallelogram
A parallelogram with adjacent sides is a Rhombus
BCAB
Special Quadrilaterals6.6
IDENTIFY SPECIAL QUADRILATERALS
ABCD is a trapezoid
Trapezoid with legs is isosceles
BCAD
Special Quadrilaterals6.6
IDENTIFY SPECIAL QUADRILATERALS
Need 4 Right angles and 4 Sides
A Rhombus with 1 right angle is a square
DCABBCAD
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
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
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
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
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
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
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
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
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
Special Quadrilaterals6.6
PROVE A QUADRIALTERAL IS A SPECIAL TYPE
PQRS is a Rectangle
A Quadrilateral with 4 right angles is a rectangle
Special Quadrilaterals6.6
HW #74Pg 367-370 8-36, 38, 40, 45-50,
53, 56-64 Even