# 5.1 Quadrilaterals - PowerPoint PPT Presentation

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5.1 Quadrilaterals. Quadrilateral :_________________________ Parallelogram :_______________________. More Parallelogram Characteristics. Theorem 5.1:____________________________ Theorem 5.2:___________________________ Theorem 5.3:___________________________. Examples. 6. y. x. 9. b.

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Parallelogram:_______________________

More Parallelogram Characteristics

Theorem 5.1:____________________________

Theorem 5.2:___________________________

Theorem 5.3:___________________________

Examples

6

y

x

9

b

80

a

x

y

9

12

a

2b

45

35

3. Find the perimeter of parallelogram PINE if PI=12 and IN=8.

P

I

12

8

N

E

A

B

F

G

D

C

E

6.

22

X=_______

y=_______

2x+18

4y-22

18

7.

X=_______

y=_______

11x

4y+5

Which to solve 1st?

45

80

• 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, XY=WZ ?

• 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.

A

B

1

7

2

8

9

10

E

6

3

4

5

D

C

A

7

2

B

1

8

F

12

10

11

9

E

6

4

3

5

D

C

A

E

B

2

8

7

9

1

3

10

5

6

4

D

F

C

5.3 Parallel Lines

Theorems involving Parallel Lines

Theorem 5.8:_______________________

_____________________________________

Theorem 5.9:____________________

__________________________________

__________________________________

Theorem 5.10:______________________

____________________________________

____________________________________

Theorem 5.11:______________________

____________________________________

____________________________________

C

R, S, T are Midpoints.

R

S

A

T

B

ABBCACSTTRRS

a)

b)

c)

12

14

18

15

22

10

5

9

6

A

R

B

S

C

T

• If RS=12 then ST=_______

• If AB=8 then BC=________

• If AC=20 then AB=_______

• If AC=10x then BC=______

C

R, S, T are Midpoints.

X

Y

A

Z

B

ABBCACXYXZZY

a)

b)

K

24

2k+3

9

8

6

5.4SpecialParallelograms

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:_______________________

_____________________________________

_____________________________________

PropertyParallelogram Rect.Rhombus Square

Examples:

ABCD is a Rhombus

A

B

62

E

C

D

M

N

29

MNOP is a Rectangle

12

L

P

O

Y

2

W

3

1

Z

X

A

B

2

1

D

E

C

5.5 Trapezoids

• 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

Trapezoids

• Trapezoid:_______________________

• _____________________________________

• ________________________

• ________________________

• Isosceles Trapezoid _____________________

• ______________________________________

Trapezoid Theorems

Theorem 5.18:______________________

__________________________________

Theorem 5.19:________________________

______________________________________

______________________________________

______________________________________

Solve: AB=10; DC=12

Find YW=_____

ZX=_____

XY=_____

10

A

B

Z

W

X

Y

C

D

12

• If AB=25, DC=13 then EF=_______

• If AE=11, FB=8 then AD=______ BC=______

• If AB=29 and EF=24 then DC=_____

• If AB=7y+6, EF=5y-3, and DC=y-5 then y=__

C

D

F

E

A

B

Find x=_______

y=_______

4

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.