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С2. Стереометрия на ЕГЭ. в формате 2010. Готовимся к ЕГЭ, формат 2010. решение. задач. с анимацией. 3. Теория. тематика задач. - скрещивающиеся:. * угол между прямой и плоскостью. • С. b. a. Прямая а лежит в α ,. •. * двугранный угол - ребро с,. В. - PowerPoint PPT Presentation

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abb b b - :* b :. II * - , .* - * - . . * ,b. ,b * . - * b - .3 ., - !DD 1. AD - . D.M MD D .) ) (D) = ( D)) - : . = + - 2 cos 4 BD - - :1) BD - . 2) BD. 3) - ! . ? ( 1)111/2 - . D D2) - . . D - ! ( )111/2 D D , . , . - . : D , D, : 15/15 D.

*** MDD 2. AD - . . 3. , - D. (), 1. - , - ! DDD , . 1). .2). .3). II .4). .5). .Cos = + - 2 cos . - ? - ? - ?3. - : ()1. = 2. (. .) ( ). = + - 2 cos cos (0,8 35/5)5 - 2, 3.. .***( , )

DD - . D DD. . -||. - D 1/211 . 61) . 2 ( 1).2) . ., , D . . : =5/2.= 3/2.3) = 13/2. , . : = + -2 CosMCKosMCK = , , . 2/6. MCK = arccos (2/6). 4. , . , . - . . . ? ! - , . , , , , : 0,7 1. D5. , 1, D . D . D . || D . , cos BKP - ? Cos . . = + - 2 cos 1201601). - ?6. D, 1, . .

D Cos TAK - ? 1/21/21/2111/2 .2). . ,1). : = = 3). : . 1/21/21/21/27 . = + - 2 cos . .

, , .

( !) = 3/4

: 1/6 . . .

.

FEBD 7-8. F 1.

DDFF11/21/21

11/2??8DDFF7) AB BC .8) F FC. 1) .2) II .3) - .1) F F .2) F II F.3) CF - 4) CF. - ? . ! - ? . ! ( ), ( ) .FC ( FCC), CF.FM = AF ( AFF),1120606060F 6 - 120: 0,9 1/2120: 90, .. Cos CFM = 0 = + -2 cos ( ) = CF + F -2 CFFcos ( )

DFF?1? AF FD. 9. F 1. DF91) F F .2) FK II F.3) DF - 4) DFK.D - ? . ! FK ( FFK).FD ( FFD), FD.12322211D = FD + FK - 2 FD FK cos DFK ( DFK). , ! D D ! F FD !(CD II AF FD ) CDF. DF, FC. 2

( , )FC = D + DF - 2 D DF cos DF. : 45 , . , . - . 8131024 D - ? D BC DABC 24 . 10 . D 13 . D . D : = = D = D =10, = D = 12. D . 101010101212D ( ). . ( ) II CB. D. KT II C, D. D.D 241013 . + D = 2D + 2. D = D + - 2 D cos D. Cos D = 01010 D. , . .D13 N D - * D.D = 676.. . , : C D ! !. - ? - !- D . D.: -|D . -,: = 8 = 27 . .66 10*. 11.90 - ? . . . ! .(C D, ) 1, 2. . , 201012 ( ) - ! |221555 .11 ... , -: = - .1 . : , 1 = 2 . . , S ACB :1/2 =1/2 . 2 2 = .5= 4/55 .= 0,8 12. . , 2, :5 D D 1. D. 2/3 12 - .2?DD 12 D D . , , D, D = 2 5, = = 10, = 45254510105555 255555, - , - .D . , - = . . 205 5 = 5 20. = 2.12 ( ) - ! 13. - . . . - , = = 5, = 5 . = 25, = 5, . - , . , - . - - . .255 . . |. ( ), |:

= 25, .( )25 - DD , = 3, = 4, = 4. DD443//, ( ). , . -? . .D - ( ),.| .| ( . 3- ) . - _ - 1. . ,52. D D . ,223. Sin = : =22 : 5.5225,( :)._ =arcsin 0,42.| . ( ). DD , = 4,D = 6, D = 6, DD , .: 0,6. , . - - . (),Tg = : .13 14. 15. - . . - ?_.. . . . ( - . 14) - 16. , = 90, = 30, = 10 3. 30 . . 3030 . 2010. AB 8 , C - AB. A, A BC 30. = 6, - , 6. .1430 = 10 3 .| , |. , . . . |.? = 30. ! . 30 2 - ? 30 = 5 3, tg 30 = 10. =103. = 102 - .88_ : = 90, . . . - _ = 30 ( ). | (. 3- ). - ? = 421. . ).2. ,tg 30 = : 3/3 = 43 : , = 12. . arctg 2/2. , 17. 18.5 3 -?16. - A . BC. . |. , = 30 - . 2 . 101 (, ) . (310)/5. 3. - A. , - . AC. - D . - , ,, 3. - . ,31053/23/23 , , - || , || ( ) : - | , ( = ), - .1) = D . . D ,D -2) = . . , -355 , = 45 .15 19. . . .. . | , . : - , - - . ( ) - .

, = = 10, = 16. 24. - . . -( ) , - ( II ). () ,PDPDB tg PDB = 16 - 20. 21 , .10101624 . .() -- . . . = , - - . BD- . ._8106 DPB. 2PB : DB FDCDABCD : = 5, AD = 12, CC = 3. BDD ADB. 2010. . 07.06. ABCDABCD : AB = 3, AD = 4, CC = 4. BDD ADD. 2010. . 07.06. 21 19. - 17664DD A D, = 6, = 6, = 4, D . DD A D, = 4, = 6, = 4, DD D. 66441. - 2. , - , 3. ( ) - D :D = D DD DD 6 4.4. D D . DD DD tgDD = 4D D . D (D ) Dtg D = DD : D 1. CDD BDA - , D2. () . 3. DO - ( . 3 - )( - , ) D - . D , tg D = D : . : 22. 23.- D ( ).D.2/32 : = : .tg D = (1213):13 ). DD 1. : D ( ), 2. : D . D - A D . . . - 18 24. . .|_|1/213 /23 /23 /22111() - = = ,. , ( ). - - .2 = , . . : 3 , = = =3 /2 . - S : = , =2 /2 . . . =2/3. . :120 DD , , = 120. , 45. . DD120|_|33 ACB ACD. DD , D. . , , 1. . - AC B D. , H. . - . - . . 221- 12019120D120 - ,90 . :DH, DH(. 3 )_DHD = 45.45 DH = DD =(3 ) : 2. DD ,DH = 3/2.S CDAB = 3/2.( . ) D, - : ? 25. 26.| 21 . 15 ABCDABCD : = 3, AD = 4, = 4. BDD D. 2010. . 07.06. - 20D4434 BDD BDDB . ADB DB- . : DB ,|DB _ - ? , . = 4. . 1 2 D = 5, DDDB554 2 AD = DB D ( ): : = 5, AD = , D4 2._ = arccos 5 3434_ = :.Cos 17 =4 ABCDAD AB = 12 , BC = 5, CC = 7. CBD D. DD1212557..: D D D. - , : D D=(D - , = D ;D = ). ! . , ! D - - , -() . . ! :D - . 137419313 - . 2- . : 74 - =193 -(13 ). = = . : cos = : =7 : 109/13 =91/109. =arccos 91/109. =2arccos 91/109. = , !!! , , - , . ? ?

.25/13,109/13, D. - 21 27. 1 2 22 2 - ( 2) . , . , - , . . . , . : . = + - 2cos : !!!hxa-x , h = S , . h , . .h: h = h h !