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1/74
2
2001- 1
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2/74
2
2001- 2
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3/74
2
2001- 3
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4/74
2
2001- 4
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8/13/2019 Unlock Geometria a Lykeiou Taexeiola Gr
5/74
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2001- 5
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2001- 6
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2001- 7
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=.
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2001- 8
y . (, ) (y, ) .
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9/74
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2001- 9
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10/74
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2001- 10
(, ).
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11/74
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2001- 11
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8/13/2019 Unlock Geometria a Lykeiou Taexeiola Gr
12/74
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2001- 12
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13/74
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2001- 13
1. , , . ;:4 :6 :8 :5 :10
2. , , , . ;:45 :10 :4 :6 :12
3. , :: :: :
4. 3
2 ,
:
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5
3
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:20 :60 :45 :35 :100
7. , i. .
ii
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14/74
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2001- 14
iii .
iv .
v .
vi .
vii .
viii .
ix , .
8. M AB O MA , :
) O AM , 2
OBOAOM
+=
) O AM , 2
OBOAOM
=
9. M AB
=
MB
MA, , O
MA . :) O AM ,
+
+=
OBOAOM
) O AM ,
+
=
OO
OM
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8/13/2019 Unlock Geometria a Lykeiou Taexeiola Gr
15/74
2
2001- 15
10. M AB,
=3
5M .
, = 3
5,
:
+
=
112.
11. , & . , =2 , :3ON = OA =+OB + O .
12. , . , = = , > 0 : = +( 1 ) .
13. ,
xOy ,
= yOA5
3xOA .
xOA x ,
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8
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y
,
.y
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16/74
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2001- 16
15.
,,AB ,
3,4,5 6 .
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.
17. ,
6
1
.
18.
,
,
. ,
120=
,
.
19. ,
,
.
==31
21
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17/74
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2001- 17
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2001- 18
(1-)
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II
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19/74
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2001- 19
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20/74
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2001- 20
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21/74
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2001- 21
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8/13/2019 Unlock Geometria a Lykeiou Taexeiola Gr
22/74
2
2001- 22
.
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180 .
.
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( )
+
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23/74
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2001- 23
.
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:
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. :
.
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2
2001- 24
1:
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> 2:
, . = 3:
,
.
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2
2001- 25
, :
.
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26/74
2
2001- 26
.
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27/74
2
2001- 27
80 30 E3
1) ;) ;
) ;) ;
2) , ;) , ;
3
.
: : 60 : 30 : 120 : 90 : 45
4 . x : : 70 : 80 : 45 : 60 : 30
Z
x
3
5
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28/74
2
2001- 28
) .
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6
, , = = . =.
7
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29/74
2
2001- 29
9
x, y, x
= y
yx
,, . , x, y , = = ,
= .
10
, = = . = .
11
(,) . x y yx
, ,
yx
, = .
12
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30/74
2
2001- 30
14
(=) =
.
,
.
15
(=) =. . :i) = ii) .
16
( 90=
) . , .
17
x
y
x
y
. x, y
= = . : = .
18
= = .
.
:)
-
8/13/2019 Unlock Geometria a Lykeiou Taexeiola Gr
31/74
2
2001- 31
) )
)
..
19
(=) , , , = . , :) )
.
20
(=)
x y y
x
.
x, y = . :) = ) .
21
xoy . , = MK = M.
22
(=), .) .
) , = .
-
8/13/2019 Unlock Geometria a Lykeiou Taexeiola Gr
32/74
2
2001- 32
23
(=)
-
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33/74
2
2001- 33
29
xy, . x, y y, x . :i) = ii) AO = iii) =
iv)
=
30
____________________
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() ,
31
. = .) .) , , , :. . . .
32
yx
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= =. , i) =
ii) =
iii)
yx
.
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34/74
2
2001- 34
33
. = .
i) AB = BE ii) =
.
34 (=).
x y yx
. ,
x , y = . i)
= ii)
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35/74
2
2001- 35
1//
2
.. : ,
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.
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36/74
2
2001- 36
, , .
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2
2001- 37
, , , .
, .
, .
-
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2
2001- 38
180=++
2
, ,
60
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39/74
2
2001- 39
-
- 2-4
- 4
-
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2
2001- 40
1 . , //.
2
= =. : ) //, ) // ) ,, .
3
1// 2 x :: 55 : 19 : 82 : 37
12x+16
254o
4
. x = , . :
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.
5
: ) 38=
74=
.
)
= 48=
) 120=+
.130=+
-
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41/74
2
2001- 41
6
60=
, =2 . : )
) ) 90=
.
7
= 2 . =. :) :i) ABE ii) .
) ,
.
8
15+=
x , 3+=
x , 65 =
x , : :> :> :>:>.
9
y
: :70 :50 :60 :30
2x
2x+10o
y 3x+40o
-
8/13/2019 Unlock Geometria a Lykeiou Taexeiola Gr
42/74
2
2001- 42
10
90=
. =
=. : ) 135=
) oyx 270=+
=
x .=
y
11
= 3 . , .
12
(=) . .
13
, 2
+
= .
14
( o90=
)
.
)
.
) : o45==
.
-
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2
2001- 43
15
= 2 90
-
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2
2001- 44
.
:i) ii) iii)
( )
i) ii)
iii) iv)
.
.
-
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45/74
2
2001- 45
.
:o .
( )
i) ii)
iii) iv)
. .
:o .o
.
( )
i) ii)
iii)
iv)
-
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46/74
2
2001- 46
:
o .o o o , ,
( ) ,
i)
ii)
iii)
iv)
v)
vi)
.
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47/74
2
2001- 47
1 2
1 2, . 1 2
, .
, .
3
2.
.
, , .
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48/74
2
2001- 48
.
.
, , , , .
.
, .
30 , .
-
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2
2001- 49
.
.
:i) ii)
i)
ii)
.
.
-
8/13/2019 Unlock Geometria a Lykeiou Taexeiola Gr
50/74
2
2001- 50
1i)
.
ii) .
iii) .
iv) .
v) , .
vi) . vii) . viii)
. ix)
. x)
. xi)
=/2.
2
, .) . .
) . .
)
:i) . ii).. iii) . .
-
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51/74
2
2001- 51
3
.
) i) .
ii) .
) iii) .
) iv)
4. :i) :: 2 : 3 : 4 : 6ii) . =5, :: 5 : 10 :15 : ,
.iii) =, : : : : : .iv)
.
=3x -2
=2x+7,
x :
: 7 : 17 : 9 : 10
-
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52/74
2
2001- 52
120
. 2x+40o
x+20o
2
3
5
=. )
. ) ,
.
6
( o90=
) . :) , .) .
) H .
7
. // // :) .) = + = + .
8
= 2. , :
) ) =) .
-
8/13/2019 Unlock Geometria a Lykeiou Taexeiola Gr
53/74
2
2001- 53
9
, = =. = , , .
10
o60=
.
)
) ;
11
. ) ) =2.
12
>
.)
) +.
13
==. .
-
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54/74
2
2001- 54
.
1
.i)
= = //.
ii)
.
iii) ( o90=
)
= /2.
iv) o90=
o30=
.
v) . vi) (//) = 2x,
= 4x, 45=
x.
vii) , .
viii) . ix) .
-
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55/74
2
2001- 55
2
:i) , , , , .) ++=+, ++ :
: + :2
+ : 2(+) : +2.
) =4+10 =+35 : : 30 : 50 : 60 : 65
ii) 90=
, , .) :: + : + : + :++) :
:2
+ :
2
+
: ++ :2
1(++)
iii) ( o90=
)
. o70=
,
:
: 30 : 45 : 60 :50 : 20.
iv) ( o90=
)
= 5 . , :: 2= : 2=3 : 4=: 3= : >.
v) (//) 90==
60=
. =20 =80, :
: 30 : 40 : 50 : 60 : 70vi) (//) 90==
, =2x =8x
-
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2
2001- 56
) :: 3x : 4x : 5x : 6x
) 30=
:
: 16 B: 12x : 8x : x3 : x32 vii) (//) , , . = 20 = 30, = y, = x
x+ y : 10 : 40 : 50 : 100.
3
o
90=
, , .
60=
, =22
3= .
60
-
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57/74
2
2001- 57
.
) i)
) ii) 3 /4
) iii) 1
) iv)
) v)
4
, , , . ,
: .4
1==
5
(
-
8/13/2019 Unlock Geometria a Lykeiou Taexeiola Gr
58/74
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2
2001- 59
10
(//) =+.
.
11
, , , , . : .
12
120=
. :) =2) =2,
) 90=
13
= 2 . , , :) ) .
14
=2.
.
) =
) =
3 .
-
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60/74
2
2001- 60
15
. , .
16
( o90=
) o30=
, . :)
)3
= .
17
(//)
o135==
. , +=.
18
(//) . .
19
(//). ,
.
.
-
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61/74
2
2001- 61
20
(//) . , :) ,
) =2
,
) , .
-
8/13/2019 Unlock Geometria a Lykeiou Taexeiola Gr
62/74
2
2001- 62
,
,
,
: .
.
.
-
8/13/2019 Unlock Geometria a Lykeiou Taexeiola Gr
63/74
2
2001- 63
,
,
.
(, R), .
.
(, R), .
-
8/13/2019 Unlock Geometria a Lykeiou Taexeiola Gr
64/74
2
2001- 64
1.
2. , (, )
60==
60=
3. (, ) (, ) ,
4. (, ) (, ) ,
5.
6. , (, )
= 2 )
= 2 ) = 2
7. (, ). 30,103 +==
)
90 110 100 40 80
)
40 20 55 45 35
-
8/13/2019 Unlock Geometria a Lykeiou Taexeiola Gr
65/74
2
2001- 65
8.
9.
3
2=
45=
)
) 2cm : 2cm B 4cm 1cm
10. .
)
= )
=
-
8/13/2019 Unlock Geometria a Lykeiou Taexeiola Gr
66/74
2
2001- 66
1
.
. :
.
2
(=) , , . .
: =
.
3
(,) .
x, y x
y ,
, x
y =.
4
>
=.
)
)
= .)
-
8/13/2019 Unlock Geometria a Lykeiou Taexeiola Gr
67/74
2
2001- 67
7 . . , , : i) ii) = iii) =.
8
ozx 20=
.35oyoz =
,
x, z =
y y . , , : i) ME=OB/2ii) MN//OA
iii)
iv)
.
9
(//)
5x 3x o
60=
. : : 11x :12x : 14x: 13x( ).
10
oo 30,90 ==
.
.
-
8/13/2019 Unlock Geometria a Lykeiou Taexeiola Gr
68/74
2
2001- 68
11
.
=- =. : i) ==ii)
iii)2
90
+=
o .
14
-
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69/74
-
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2
2001- 70
) . .
19
xxxx 4,3,2, ====
. x.
;( ).
20
(=)
o120=
.
; ;
21
, =. : ) .)
) = 2
1.
22
oo 60,90 ===
. ,
, =8, =2 : ) ) =4)
.
-
8/13/2019 Unlock Geometria a Lykeiou Taexeiola Gr
71/74
2
2001- 71
23
(//) =20 =40. , , , , , .
24
o120=
=12. .
25
>. = =, ) ) -
-
8/13/2019 Unlock Geometria a Lykeiou Taexeiola Gr
72/74
2
2001- 72
28
o90==
, , . ) )
.
29
o120=
=2.
)
) o90=
.
30 (//) =2
) , , =2
3
) ) , ,
2
= .
-
8/13/2019 Unlock Geometria a Lykeiou Taexeiola Gr
73/74
2
2001- 73
-
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74/74
2
