Post on 14-Jan-2016
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5.1
Quadrilaterals
Quadrilateral:_________________________
Parallelogram: _______________________
More Parallelogram Characteristics
Theorem 5.1:____________________________
Theorem 5.2:___________________________
Theorem 5.3:___________________________
Examples
______
______
______
______
a
b
x
y
6
9b
a
80
xy
xy
4535
______
______
______
______
a
b
x
y
9
2b
12a
3. Find the perimeter of parallelogram PINE if PI=12 and IN=8.
P I
NE
12
8
4. : ABCD and CEFG
Prove: A F
Given
A B
C
GF
DE
1.
2. Opp 's
3. Transitive
Given
2x+18
184y-22
22 X=_______
y=_______
6.
7. 11x
4580
4y+5
X=_______
y=_______
Which to solve 1st?
True or False:
1.Every parallelogram is a quadrilateral?
2.Every Quad is a parallelogram?
3.All angles of a parallelogram are congruent?
4.All sides of a parallelogram are congruent?
5. In RSTU, RS is parallel to TU?
6. In XWYZ, XY=WZ ?
7. In ABCD, if angle A=50, then C=130?
5.2
Proving Parallelograms
Ways to Prove Quadrilaterals are Parallelograms
Theorem 5.4: _____________________________
________________________________________
Theorem 5.5: _____________________________
________________________________________
Theorem 5.6: _____________________________
________________________________________
Theorem 5.7: _____________________
___________________________________
5 ways to prove a quad is a Parallelogram
1.
2.
3.
4.
5.
: ; BE=DE
Prove : is a
Given AD BC
ABCD
A
C
1. 1. Given
B
D
E
12
56
87
43
9 10
: ;
CF bisects BCD
AE bisects BAD
Prove :
Given ABCD
AE CF
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��������������
A
C
1. 1. Given
B
D
E
12
56
87
43
910
F
1112
: ; 9 10
Prove : is a
Given AECF
ABCD
A
C
1. Here are the Reasons 1. Given
F
B
D
E
12
10 5 6
8 7 9
43
5.3
Parallel Lines
Theorems involving Parallel Lines
Theorem 5.8: _______________________
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Theorem 5.9: ____________________
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Theorem 5.10: ______________________
____________________________________
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Theorem 5.11: ______________________
____________________________________
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C
R
A T B
S
R, S, T are Midpoints.
AB BC AC ST TR RS
a)
b)
c)
12 14 18
15 22 10
5 9 6
R
S
T
A
B
C
1. If RS=12 then ST=_______
2. If AB=8 then BC=________
3. If AC=20 then AB=_______
4. If AC=10x then BC=______
C
X
A Z B
Y
R, S, T are Midpoints.
AB BC AC XY XZ ZY
a)
b)
K 2k+324
9 68
5.4
SpecialParallelograms
Special Parallelograms
Rectangle:___________________________
Rhombus:___________________________
Square: _____________________________
Theorems for Special Parallelograms
Theorem 5.12: ______________________
___________________________________
Theorem 5.13:_______________________
___________________________________
Theorem 5.14: _______________________
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Theorem 5.15: _____________________
___________________________________
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Proving a Rhombus or Rectangle
Theorem 5.16: _______________________
_____________________________________
_____________________________________
Theorem 5.17: _______________________
_____________________________________
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Property Parallelogram Rect. Rhombus Square
Opp sides
Opp sides
Opp 's
Diag form
Diag bisectDiag
Diag
Diag bisect 2 's
All Rt 's
All sides
Examples:
ABCD is a Rhombus
A B
CD
62
_______
_______
_______
_______
ACD
DEC
EDC
ABC
E
M N
P O
LMNOP is a Rectangle
______
______
_________
________
PON
PMO
PL
MO
29
12
1
2
3
2 3; Find 1=______
YW=3x-2 ; WZ=x+8; Find YZ=_____
W
Y
ZX
: ; BE=CD
1 2
Prove : is a Rhombus
Given ABCD
ABCD
A
C
1. 1. Given
B
D E12
5.5
Trapezoids
Warmup: Always, Never or Sometimes
1.A square is________ a rhombus.
2.The diagonals of a parallelogram _________ bisect the angles of a parallelogram.
3.The diagonals of a rhombus are _________ congruent.
4.A rectangle _________ has consecutive sides congruent.
5.The diagonals of a parallelogram are _________ perpendicular bisectors of each other
Trapezoids
Trapezoid: _______________________
_____________________________________
•________________________
•________________________
Isosceles Trapezoid _____________________
______________________________________
Trapezoid Theorems
Theorem 5.18:______________________
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Theorem 5.19: ________________________
______________________________________
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______________________________________
A B
CD
X YZ W
Solve: AB=10; DC=12
Find YW=_____
ZX=_____
XY=_____
10
12
AB
C D
F E
1. If AB=25, DC=13 then EF=_______
2. If AE=11, FB=8 then AD=______ BC=______
3. If AB=29 and EF=24 then DC=_____
4. If AB=7y+6, EF=5y-3, and DC=y-5 then y=__
4
x
y
Find x=_______
y=_______
Quad TUNE is an isosiceles trapezoid with TU and NE as bases. If angle U equals 62 degrees find the measures of the other 3 angles.
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______
______
E
T
N