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# 5.1 Quadrilaterals - PowerPoint PPT Presentation

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: _______________________

Theorem 5.1:____________________________

Theorem 5.2:___________________________

Theorem 5.3:___________________________

6

y

x

9

b

80

a

x

y

9

12

a

2b

45

35

P

I

12

8

N

E

A

B

F

G

D

C

E

6. IN=8.

22

X=_______

y=_______

2x+18

4y-22

18

7.

X=_______

y=_______

11x

4y+5

Which to solve 1st?

45

80

• True or False: IN=8.

• 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 IN=8.Proving Parallelograms

Theorem 5.4: _____________________________

________________________________________

Theorem 5.5: _____________________________

________________________________________

Theorem 5.6: _____________________________

________________________________________

___________________________________

5 ways to prove a quad is a Parallelogram

1.

2.

3.

4.

5.

A IN=8.

B

1

7

2

8

9

10

E

6

3

4

5

D

C

A IN=8.

7

2

B

1

8

F

12

10

11

9

E

6

4

3

5

D

C

A IN=8.

E

B

2

8

7

9

1

3

10

5

6

4

D

F

C

5.3 IN=8.Parallel Lines

Theorem 5.8: _______________________

_____________________________________

__________________________________

__________________________________

____________________________________

____________________________________

____________________________________

____________________________________

C IN=8.

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

A IN=8.

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 IN=8.

R, S, T are Midpoints.

X

Y

A

Z

B

AB BC AC XY XZ ZY

a)

b)

K

24

2k+3

9

8

6

5.4 IN=8.SpecialParallelograms

Rectangle:___________________________

Rhombus:___________________________

Square: _____________________________

Theorem 5.12: ______________________

___________________________________

Theorem 5.13:_______________________

___________________________________

Theorem 5.14: _______________________

___________________________________

___________________________________

___________________________________

Theorem 5.16: _______________________

_____________________________________

_____________________________________

Theorem 5.17: _______________________

_____________________________________

_____________________________________

Examples: IN=8.

ABCD is a Rhombus

A

B

62

E

C

D

M IN=8.

N

29

MNOP is a Rectangle

12

L

P

O

Y IN=8.

2

W

3

1

Z

X

A IN=8.

B

2

1

D

E

C

5.5 IN=8.Trapezoids

• Warmup IN=8.: 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 IN=8.

• Trapezoid: _______________________

• _____________________________________

• ________________________

• ________________________

• Isosceles Trapezoid _____________________

• ______________________________________

Trapezoid Theorems IN=8.

Theorem 5.18:______________________

__________________________________

______________________________________

______________________________________

______________________________________

Solve: AB=10; DC=12 IN=8.

Find YW=_____

ZX=_____

XY=_____

10

A

B

Z

W

X

Y

C

D

12

C

D

F

E

A

B

Find x=_______ IN=8.

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.