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ΒΟΗΘΗΜΑ ΓΕΩΜΕΤΡΙΑΣ Α ΛΥΚΕΙΟΥ ΘΕΩΡΙΑ ΑΣΚΗΣΕΙΣ

• 2

2

:

(,- , ).

( , , , ).

taexeiola.gr

• 10. 1

1

taexeiola.gr

• 11. 1

taexeiola.gr

• 12. 1

taexeiola.gr

• 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

taexeiola.gr

• 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

taexeiola.gr

• 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

taexeiola.gr

• 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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