5.1 Quadrilaterals

1
5.1 Quadrilaterals
2
Quadrilateral_________________________ Parallelo
gram _______________________
3
More Parallelogram Characteristics
Theorem 5.1____________________________ Theorem
5.2___________________________ Theorem
5.3___________________________
4
Examples
6
x
y
9
b
80
a
x
y
9
12
a
2b
45
35
5
3. Find the perimeter of parallelogram PINE if
PI12 and IN8.
P
I
12
8
N
E
A
B
G
F
D
C
E
6
6.
22
X_______ y_______
2x18
4y-22
18
7.
X_______ y_______
11x
4y5
Which to solve 1st?
45
80
7

• True or False
• Every parallelogram is a quadrilateral?
• Every Quad is a parallelogram?
• All angles of a parallelogram are congruent?
• All sides of a parallelogram are congruent?
• In RSTU, RS is parallel to TU?
• In XWYZ, XYWZ ?
• In ABCD, if angle A50, then C130?

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5.2 Proving Parallelograms
9
Ways to Prove Quadrilaterals are Parallelograms
Theorem 5.4 _____________________________ _______
_________________________________ Theorem 5.5
_____________________________ ___________________
_____________________ Theorem 5.6
_____________________________ ____________________
____________________
10
Theorem 5.7 _____________________ _______________
____________________
5 ways to prove a quad is a Parallelogram 1. 2.
3. 4. 5.
11
A
B
1
7
2
8
9
10
E
6
3
4
5
C
D
12
A
7
2
B
1
8
F
12
10
11
9
E
6
4
3
5
C
D
13
A
B
E
2
8
7
9
1
3
10
5
6
4
C
F
D
14
5.3 Parallel Lines
15
Theorems involving Parallel Lines
Theorem 5.8 _______________________ _____________
________________________
16
Theorem 5.9 ____________________ ________________
__________________ _______________________________
___
17
Theorem 5.10 ______________________ _____________
_______________________ __________________________
__________
18
Theorem 5.11 ______________________ _____________
_______________________ __________________________
__________
19
C
R, S, T are Midpoints.
R
S
A
T
B
AB BC AC ST TR RS a) b) c)
12
14
18
15
22
10
5
9
6
20
R
A
S
B
T
C

1. If RS12 then ST_______
2. If AB8 then BC________
3. If AC20 then AB_______
4. If AC10x then BC______

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C
R, S, T are Midpoints.
X
Y
A
Z
B
AB BC AC XY XZ ZY a) b)
K
2k3
24
9
6
8
22
5.4SpecialParallelograms
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Special Parallelograms
Rectangle___________________________ Rhombus___
________________________ Square
_____________________________
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Theorems for Special Parallelograms
Theorem 5.12 ______________________ ____________
_______________________ Theorem
5.13_______________________ _____________________
______________ Theorem 5.14 ____________________
___ ___________________________________
25
Theorem 5.15 _____________________ ______________
_____________________ ____________________________
_______
26
Proving a Rhombus or Rectangle
Theorem 5.16 _______________________ ____________
_________________________ ________________________
_____________ Theorem 5.17 _____________________
__ _____________________________________ _________
____________________________
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Property Parallelogram Rect. Rhombus
Square
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Examples
ABCD is a Rhombus
A
B
62
E
C
D
29
M
N
29
MNOP is a Rectangle
12
L
P
O
30
Y
2
W
3
1
Z
X
31
A
B
1
2
D
E
C
32
5.5 Trapezoids
33

• Warmup Always, Never or Sometimes
• A square is________ a rhombus.
• The diagonals of a parallelogram _________ bisect
  the angles of a parallelogram.
• The diagonals of a rhombus are _________
  congruent.
• A rectangle _________ has consecutive sides
  congruent.
• The diagonals of a parallelogram are _________
  perpendicular bisectors of each other

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Trapezoids

• Trapezoid _______________________
• _____________________________________
• ________________________
• ________________________
• Isosceles Trapezoid _____________________
• ______________________________________

35
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36
Trapezoid Theorems
Theorem 5.18______________________ ______________
____________________
37
Theorem 5.19 ________________________ ___________
___________________________ ______________________
________________ _________________________________
_____
38
Solve AB10 DC12 Find YW_____
ZX_____ XY_____
10
A
B
Z
W
X
Y
C
D
12
39

1. If AB25, DC13 then EF_______
2. If AE11, FB8 then AD______ BC______
3. If AB29 and EF24 then DC_____
4. If AB7y6, EF5y-3, and DCy-5 then y__

C
D
F
E
A
B
40
Find x_______ y_______
4
x
y
41
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.