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

��������������

��������������

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: _______________________

_____________________________________

Theorem 5.9: ____________________

__________________________________

__________________________________

Theorem 5.10: ______________________

____________________________________

____________________________________

Theorem 5.11: ______________________

____________________________________

____________________________________

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: _______________________

___________________________________

Theorem 5.15: _____________________

___________________________________

___________________________________

Proving a Rhombus or Rectangle

Theorem 5.16: _______________________

_____________________________________

_____________________________________

Theorem 5.17: _______________________

_____________________________________

_____________________________________

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:______________________

__________________________________

Theorem 5.19: ________________________

______________________________________

______________________________________

______________________________________

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.

______

______

______

E

T

N