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ΒΟΗΘΗΜΑ ΓΕΩΜΕΤΡΙΑΣ Α ΛΥΚΕΙΟΥ ΘΕΩΡΙΑ ΑΣΚΗΣΕΙΣ

Transcript of ’——œ‘ “•©œ•¤™‘£...

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    2

    :

    (,- , ).

    ( , , , ).

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  • 10. 1

    1

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  • 12. 1

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  • 13. 2

    .

    2003.

    . 14: 1, 2

    . 20: 1

    1,2, 3

    1

    . 25:

    1

    . 28: 3, 4

    1,2, 3

    . 30: 4, 5

    1

    "" 2

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  • 14. 3

    1. , , , = 2

    = 2. : 2

    = +

    :

    1

    2 2

    = = .

    , :1

    22

    = = (1)

    1

    2 3 3 3

    = + = = = (2)

    : (2) 2

    2 3

    = = (3)

    2 22 8 82 2 2 3 3 32 82

    2 2 3 33

    = = = =

    + + + ...

    2. , , , , ,

    , , . :

    . +

    =2

    . = , .

    :

    . :

    2 2

    = + + = + + =

    1

    2

    3

    A B

    A B

    taexeiola.gr

  • 15. 3

    ( ) 2 2 2 2

    + + + + + += = =

    . :

    = + = + = .

    2 2

    = + = + = + = + =

    3.

    .

    :

    : ( )90 : ( )180 ( ) ( ) 180 90 180 90 90 = + =

    4.

    52 .

    :

    ( ) ( ) ( ) o o 5180 90 2 180 5 90 360 2 450 52

    = = =

    5 2 450 360 3 90 30 = = =

    5. 3 , , ,

    . x, y, Oz

    Oy A , , , , -

    : xOz = .:

    : o y yB 90 yB y y = = = = B = (1)

    A B

    taexeiola.gr

  • 16. 3

    (1) AB

    xy xB By y y z y yz2 2

    = + = + = + = + =

    y xz .

    xy yz2

    = = . :

    ( ) o o B 2x 2 y xy 2 90 180 2

    = = = =

    (1) 180 = .

    ( ) 180 2 180 2 180 = = = 180 360 2 2 180 + = : 2 180 0 90 > > .

    6. AOB, AO AOB x,y .

    AOB AO . xOy OB O .

    :

    : AOB AO

    xOy2

    =

    :

    AOB AO AOB AO xOy xO yOA

    2 2 2

    = = =

    OB O oBO 90= , :o

    o AOB AO BO 90

    xOy 452 2 2

    = = = =

    7. , , .

    , A ,

    AB +

    =2

    A +

    =2

    .

    y B

    x

    A

    z

    O

    y

    B

    x

    A

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  • 17. 3

    A

    N

    BO

    M

    A

    N

    BO

    M

    :

    1 :

    , . :

    A

    2 2

    = + + = + + =

    ( ) A 2 A AB 2 2 2

    + + + + + += = =

    2 :

    , . :

    A

    AB2 2

    = = = =

    ( ) ( ) 2AB A AB AB A A 2 2 2

    + += =

    taexeiola.gr

  • 18. 4

    1. :

    . 1/9

    .

    .

    10/9 .

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    2. xy O O

    x y . -

    xy ,

    O O .

    ............................................................................................................................

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    1

    2

    3

    4

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  • 19. 4

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    3. ,, O

    . O :

    . O O .

    . O O .

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    4. ,

    . 90, -

    45.

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    taexeiola.gr

  • 20. 4

    ............................................................................................................................

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    5.

    3 = 5 .

    3 - 5

    =8

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