Upload
kiklades1209
View
228
Download
0
Embed Size (px)
Citation preview
8/11/2019 111-136
1/26
8
.
,
, .
,
.
,
.
, .
, .
A
A( )1 ( )2
A
A
B
8/11/2019 111-136
2/26
112. -
. , 30
.
i)
.. .
ii) .
, .. .
iii)
.. , .
iv) , .. .
v) , .
vi) ,
. .
:
-
.
, .
.= 1 2
( , , )= = = ,
= = . -
,
.
2 2 2
+ += = = .
-
.
. .
1
2
2
1
8/11/2019 111-136
3/26
8/11/2019 111-136
4/26
114. -
.
1 -
.
, ,
, , .
EZ B , ,
. ( )
12= , .
( )
22
=
. (1) (2) = , .
2
,
,
= 90 .
( ) 1= +
, , 90= .
, ( )
22
+= . (1),
(2)
2=
, . 90= .
3
, -
,
, .
1 1AA 1 : ( )1 11 12+
= .
8/11/2019 111-136
5/26
115. -
1 1
: ( )1 11
2
2
+= .
(1), (2) :
1 1 1 1
1
2
2
+ + +=
1 1 1 1 14 = + + + .
4
-
.
, .
, , , ,
. , , :
2 1
3 3= = (1)
, , :
2 1 3 3
= = (2)
(1) (2) :1
3
= = = .
5
. .
, :3
2 =
. //
, . = .
// , . = .
2
2 3
= + = = .
B
H
K
A
B
H
K
A
B
H
A
B
H
K
A
()
11111
8/11/2019 111-136
6/26
116. -
6
= 3 0 .
,
.
, .
.
30=
2
= .
2
= (-
. ). -
.
0 0
1 1 2 2 30 60 = = = = ,. = .
= .
7
, . .
, -
.
2
= =
2
= =
= .
.
8
. .
1 2
= ,
2 1
= , //.
1 1
= ,.
2
= = .
-
.
B
K
M
A
B
K ZO
A
21
1
B
K ZO
A
B
H
K
A
8/11/2019 111-136
7/26
117. -
9
1
= 4 .
.
//4
= .
. 1
4
= = .
//2
= ( , , )
//
2= ( , , ).
2 // //
2 2 4= = = .
10
( = 9 0 ) .
.
2= = .
1 1
= .
-
2
= = . 2 2
= .
,-
:1 2 1 2
+ = + 90= = .
11
,
. , , , , ,
.
BI
A
Z
1
1
2
2
B
I
A
B
I
A
8/11/2019 111-136
8/26
118. -
A K B
AB
KM 2=
2
= . =
=
( )
( )
1
2
= +
= +
1 1
K 90
= =
= =
=
=. (1), (2) =
=
= ( )
1 1
= ( )
=
=
.
12
. , = - .
90 = = = .
= ,
1
2
= = .
13
= = = .
. :
i.
ii.
A
1
1
K
NM
A
B
K
E
A
B
K
E
8/11/2019 111-136
9/26
119. -
=
:
=
= =
=
=
= . = .
.
i.
, , , .
//2
=
//2
=
= = .
-
, .
ii. , , , .
//
//
. 90=
14
, > .
.
= -
1 1
= ( 1
1
=
A
K
M
N
A
K
M
N
A
K
M
N
A
B K
E
M
8/11/2019 111-136
10/26
120. -
( ).
1
= ( //).
= .
15
(//, > ) -
. , ,
.
.
2
= .
.
2= .
= =
2 2 2
=
,
2
= .
=
16
( //)
= 2 = 3 . .
:
. O .
. .
. ,
: = /4.
A
B K
E
M1 1
A
O
B
P
A
H O
8/11/2019 111-136
11/26
121. -
. 180 3 180 45+ = + = = .
135= . . = = /2,
. -
, -
.
. , .
1
45= = 90= . = /2 = .
, , .
. , :
1 1
2 2 2 4
= = = .
17
o
= 6 0
.
.
1 2
1
2 1
30
( )
= = =
=
-
.
: 1
30 2
= =
.
18
(//) = + .
. .
.
//
2 2
+= = . = = .
B
P1
1
A
H O
A
K
B
1
1
2
8/11/2019 111-136
12/26
122. -
1
= 1
= ( // ). = .
2
= 2
= ( // ), = .
19
( ) = = 90 = 6 0 . = = 8 .
.
1
90 90 60 30= = = .
8
42 2
= = =
8 4 12= + = + = + =, , :
12 8 20 10
2 2 2
+ += = = =
20
( ) = 90 = 30 . ,
, = .
30=
2
= .
, ,
2
= .
= .
B
K
A
12
A
K
B
1
E
60o
B
A
Z
30o
8/11/2019 111-136
13/26
123. -
21
. , , ,
= . , , , , , .
-
.
AK (1)2
= .
( )
22
= . = (3)
= ( = - = ).
(1), (2), (3) = .
=
:
=
= ,
1 1 =
= .
.
= =
= =
, .
. . , ,
.
22
( ) = 90 = 30 , . = .
.
, , ,
||2
=
EA
K
Z
1
1
8/11/2019 111-136
14/26
124. -
2 // = = .
. 30= ,
2
= = ,. .
23
o
= 4 5 . .
.
,
(1)
2=
,
(2)2=
(1),(2) =
.
1 2
90 90= + =
( = ) :
1 1 1 1
180 180 2 + + = = =
( = ) :
2 1 2 1
180 180 2 + + = = =
:
1 2
180 2 180 2 360 2( )+ = + = +
180 180 45 135+ = = =
1 2
360 2 135 90+ = = .
24
= 30
A
E
2
1
2
1
1
B
A
30o
8/11/2019 111-136
15/26
125. -
B
A
30o
. :
i. = ii.
=3 .
i. =
,
90 , ,
2
= = = =
.
= .
ii. . ( ) 90 , 30 := =
2
2
= = .
= , :
3 3
+ = = .
25
// = 4.
i. 5B
=2
.
ii. ,, = = = , , .
iii. , ,
=2
.
i. 4 5
2 2 2
+ += = = .
ii. 1 4
= = //
.
1
4
= = //
.
iii. , , .
// = , // = .
= =5
2 2
= .
A
H
K
Z
8/11/2019 111-136
16/26
126. -
26
= 4. , = = .
i. .
ii. .
i. // //. -
. = .
=
= = . = .
ii. ,
2 2
+ += = .
= = 4
= = 4 = 2.
4 2 6
32 2
+= = = .
27
. , -
, .
1
90= = = .
.
2
2
=== -
.
-
// // 2
= =
.
EA
Z
K
A
M
E
8/11/2019 111-136
17/26
127. -
28
( = ), , , ,
.i. .
ii. , .
i.
// //
2
= =
. = .
= = = . .
ii.
// 2
=
.
2
3
= ( )
2
13 2 2 3
= = = .
1
3
= .
// = .
1
3
= 1
3
= = (
) = . (
).
29 . , -
, , = .
:
// , // 2
=
.
A
E
Z
8/11/2019 111-136
18/26
128. -
:
( )
// 1 , / / 2
=
.
,
= ( ).
( )
// 2 . 2
=
(1),(2) // = , .
= = .
30
o
= 90 , , , ,
. :
i.
H =4
ii. .
i.
2
=
, -
2
= =
1 1
=
, -
2
= =
2 2
=
1 2 1 2
90= + = + = =
2
2 2 4= = =
A
O
Z
K
A
H 2
1 2
Z
1
8/11/2019 111-136
19/26
129. -
ii. :
2 2 2 2
+ ++ + = + + = .
31
. -
. , ,
:
i. //
ii. ( )
iii. .
i. : 90= = =
( 90= - ).
, ( )1 1
1= = .
( )
( )2 1
2= x .
(1), (2) 2 1
= . //
x .
ii. (1 2
= ), ( )
.
2
2
=
= = .
.
iii. 30
2= =
90 60= =
:
1 1
180 60 60
2
= = =
2 1
2 1
90 90 60 30
180 180 60 120
= = =
= = =
A
O
Z
H
x
2
2
2
1
1 1
1
8/11/2019 111-136
20/26
130. -
32
.
.
//.
, 2
= = = -
.
1 1
45= =
.
360 90 90 180 = =
:
( )2 2
180 180 180 180 180
2 2 2 2
+= = = = =
45 45 90 902 2 2 2 2
++ = + + + = + + = +
180+ =
180
90 1802
+ = + =
,
, //, .
= .
33
-
i.
ii. .
i.
4 2 3 1
360 360 90 60 90 120= = =
A
E
K Z2
/2
2 /21
1
8/11/2019 111-136
21/26
131. -
=
.
1 1 4 1
180 2 120 180+ + = + =
1 1
60 2 180 120 60 30
2= = = =
4 1 1
120 , 30 , 30= = =
ii.E
1 2
45 60 105= + = + =
(
1 45= 90=
2 60=
)
2 1
45 30 75= + = + =
2 45=
90=
,
105 75 180+ = + = //
.
= .
34
,
=2
=2
.
.
// 2
= =
//
2
= =
1
90 = + . 1
= ,
,
.
90 = + (1)
E
A4
K
1 1
1
1 1
2
2
22
3
A
I
K1 1
1
12
8/11/2019 111-136
22/26
132. -
1
90 = + . 1
= , ,
. 90 = + (2)
(1), (2) =
. = , = , =
= ( - - ). = ,
.
:
1 1 1 1 1
180 90 180+ + = + + + =
1
1 1 1 1 1
90 90
=
+ + = + + = (3)
=
// //
2
= =
1 2
=
.
: (3) 1 2
90 90
+ + = =
14
(//) , , , , ,
. : EZ H .
EZ H ,
E // = EH E= . , -
, ( )
EH // 12
= .
( )
// 2
2
= .
(1) (2) : EH //= ,
. ,
, ( )
// 32
= .
, , ( ) 4= .
(1), (3) (4) : EH E= .
EZ H .
BA
H
Z
E
8/11/2019 111-136
23/26
133. -
.
1. >
x A x.
,
:
.-
2
=
. -
2
.
902
.
2. 30 135 ,-
,
.
.
3. / = 2.
, - .
4. // = 2.
-
, . = = .
5. , -
, -
.
, :
. = + .
2
=
.
2
B
H
K
x
A
BH K1530
A
BK
A
B
K ZOH
A
B
I
A
8/11/2019 111-136
24/26
8/11/2019 111-136
25/26
135. -
.
,
( ).
+ = 4 .
8/11/2019 111-136
26/26