5.1
This presentation is the property of its rightful owner.
Sponsored Links
1 / 41

5.1 Quadrilaterals PowerPoint PPT Presentation


  • 114 Views
  • Uploaded on
  • Presentation posted in: General

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

Download Presentation

5.1 Quadrilaterals

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


5 1 quadrilaterals

5.1 Quadrilaterals


5 1 quadrilaterals

Quadrilateral:_________________________

Parallelogram:_______________________


5 1 quadrilaterals

More Parallelogram Characteristics

Theorem 5.1:____________________________

Theorem 5.2:___________________________

Theorem 5.3:___________________________


5 1 quadrilaterals

Examples

6

y

x

9

b

80

a

x

y

9

12

a

2b

45

35


5 1 quadrilaterals

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


5 1 quadrilaterals

6.

22

X=_______

y=_______

2x+18

4y-22

18

7.

X=_______

y=_______

11x

4y+5

Which to solve 1st?

45

80


5 1 quadrilaterals

  • 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 1 quadrilaterals

5.2 Proving Parallelograms


5 1 quadrilaterals

Ways to Prove Quadrilaterals are Parallelograms

Theorem 5.4: _____________________________

________________________________________

Theorem 5.5: _____________________________

________________________________________

Theorem 5.6: _____________________________

________________________________________


5 1 quadrilaterals

Theorem 5.7:_____________________

___________________________________

5 ways to prove a quad is a Parallelogram

1.

2.

3.

4.

5.


5 1 quadrilaterals

A

B

1

7

2

8

9

10

E

6

3

4

5

D

C


5 1 quadrilaterals

A

7

2

B

1

8

F

12

10

11

9

E

6

4

3

5

D

C


5 1 quadrilaterals

A

E

B

2

8

7

9

1

3

10

5

6

4

D

F

C


5 1 quadrilaterals

5.3 Parallel Lines


5 1 quadrilaterals

Theorems involving Parallel Lines

Theorem 5.8:_______________________

_____________________________________


5 1 quadrilaterals

Theorem 5.9:____________________

__________________________________

__________________________________


5 1 quadrilaterals

Theorem 5.10:______________________

____________________________________

____________________________________


5 1 quadrilaterals

Theorem 5.11:______________________

____________________________________

____________________________________


5 1 quadrilaterals

C

R, S, T are Midpoints.

R

S

A

T

B

ABBCACSTTRRS

a)

b)

c)

12

14

18

15

22

10

5

9

6


5 1 quadrilaterals

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=______


5 1 quadrilaterals

C

R, S, T are Midpoints.

X

Y

A

Z

B

ABBCACXYXZZY

a)

b)

K

24

2k+3

9

8

6


5 1 quadrilaterals

5.4SpecialParallelograms


5 1 quadrilaterals

Special Parallelograms

Rectangle:___________________________

Rhombus:___________________________

Square: _____________________________


5 1 quadrilaterals

Theorems for Special Parallelograms

Theorem 5.12: ______________________

___________________________________

Theorem 5.13:_______________________

___________________________________

Theorem 5.14: _______________________

___________________________________


5 1 quadrilaterals

Theorem 5.15:_____________________

___________________________________

___________________________________


5 1 quadrilaterals

Proving a Rhombus or Rectangle

Theorem 5.16:_______________________

_____________________________________

_____________________________________

Theorem 5.17:_______________________

_____________________________________

_____________________________________


5 1 quadrilaterals

PropertyParallelogram Rect.Rhombus Square


5 1 quadrilaterals

Examples:

ABCD is a Rhombus

A

B

62

E

C

D


5 1 quadrilaterals

M

N

29

MNOP is a Rectangle

12

L

P

O


5 1 quadrilaterals

Y

2

W

3

1

Z

X


5 1 quadrilaterals

A

B

2

1

D

E

C


5 1 quadrilaterals

5.5 Trapezoids


5 1 quadrilaterals

  • 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


5 1 quadrilaterals

Trapezoids

  • Trapezoid:_______________________

  • _____________________________________

  • ________________________

  • ________________________

  • Isosceles Trapezoid _____________________

  • ______________________________________


5 1 quadrilaterals

Trapezoid Theorems

Theorem 5.18:______________________

__________________________________


5 1 quadrilaterals

Theorem 5.19:________________________

______________________________________

______________________________________

______________________________________


5 1 quadrilaterals

Solve: AB=10; DC=12

Find YW=_____

ZX=_____

XY=_____

10

A

B

Z

W

X

Y

C

D

12


5 1 quadrilaterals

  • 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


5 1 quadrilaterals

Find x=_______

y=_______

4

x

y


5 1 quadrilaterals

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.


  • Login