Tìm hiểu sâu thêm ĐL Mê-Nê-La-Uýt (C. N)

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 !    )  +          !     +  !  %        +  )  #  *  +      %   !    0(    %          #    )  ."     "  .       !(  +  '+#'+    #  ..  #  .  !    & .)%  %  "  "      "  "    .  *  "  "  ')  !          (    1  "     )  +  "           #      "  "   !%        )  .')#      !(    (  "  !       2     3    "  &      " %    #"       ")  +      &!  "%  +)        &  "        "   4    +  4  %  )    %    5%  %  )  +     "%  "         ""      %      !"        6      +  7 +8&  "  .  ("  )    +  7+#"      !  &              %     9&      +  7+#  6+      8   %  )+  "    +    # .    #%    .'      %    )     +5  )           !  !&  :"      +  7+  ; 5  )  '    +              %     ;<.)      &        %             )  '          %     <   +    '++  %  !&        &  %    )    +!  %    &  7+"  ; <    7+  )  #  .    .          +     (   '%    .    .          +      %          !!%  .   35="  %  '    '      #        %  )  '      #  !  )+)  +  %  )     (#  >?@      +# ""    ("        +     +    %      #$("    "      )  #         +  1(#  +  >"          )      !*  !%  '  +    "%  # )  +    +  "  !   )  .#&               "      %      %  "   "          #  +  %  "        3      "       <A5B  &  #   +%            !          #   #&  )  '  !)    !    .  <)+  "    !)  +  " !      6      "     8 !  .      C  !(  C#"    !(    %           3      )  +#   .  %    +!  #&  %    "     )  .  )  + !#    9    "  )        #  ("  + +%  #%  "  #.    "    "  &  +!  !$(")      +  *%      )        !    !  !        %  %   >    +  )  .*  #"  ")"#'        )  .'    "     "  "          .    "#"          <  +  7 +    .'          %             <)+%    "  %  "   "        ("  )  .35=!       "  "%    !  "    #       7    !    !  35=1  !  )+    +   DE  .%     F  )  .      "        #  !  '  +       %     F    +    ')  +%  %  "        #+&     "            .  +'+    !   F    +      )         2DE  .%     FG)      !        %    9     "%  #&  )    )#  .)            )  %  " F=+)  %      (  "#          "#)  .)    &  #  %  $  )  +  )    "  "    #+%  !)      "  +"   F!%    +    %       3%  (   !  !  #%  $  #     %      +  #)&       #   &  "&  .  .)      +    "!)+ "  '  !       +#      )  +      9  "  )  .  +%      #         ".  !    "    9  "    !           *H&"  '  +"     !  35=1  # &      &"  2IIJ2IIK "  $  %%%$"    &     -  )+    '<  +              (  &  "  . )  +      '    +  <)+      .  .%         ..  .+%  )&        6      ()  .    '            ('  8#+  )  .  *(  "  #%    ".  !    "  #     )        &    !    "        "         )  %  "  "        '(  )  *%*%)%+, <A5B 2 5"  LM5    "7##>!    &        M5#5L# LM&      "&  "!.)  (  '      4&  "    "&  " !.)  (  '    "    #    "&  "!    "  <     )        7##>&        =       68 5  " !    .!  "7##>      "      "  #      >     ?    7##>&       "68 9(  M-DDL56- ∈ 78           == 4 =+!  ==             6."8         #    #>&  "!   L5  LM  "  LM547&  "!.)  (   '    M5?  7N    "  >  M5#+! 7N&  "!.)  (  '    M568 E%  7N##>&                       =⇒== N N  N N 628   68  628+!  ≡ N 3+  "7##>&     !    .25    "7##>  &  "!.)  (  '        "    -&  (,.  /0.    1 M    5"  LM5#(  !+  M-6- ∈ L58!LM)  +"     ":L:O2M:45:&  M-  P5  "  Q  =  1           ! "#$ ?  7  !  "  L:#+!-7    !%    "  L:5  DD ⇒    2   =  ⇒ :PDD7- ⇒ P  !  "   M- ⇒ :P    !%    "  M7- ⇒ Q2   == 6."8   %    ! "#$ 0(  "  :L5    "M#P#-&        Q  R   =⇒==⇒=             6."8 <A5B R P A B C M N D F B A C D E M M    25"  LM5#7  !  "  M57    &  *7    .)      ML5&  L5#LM)      :  P5  " !&  5:OMP 1           ! "#$   &  &      L-DDP7  7:DDL-     =⇒ 684     = 628 7&    (%  )    .)         = 6R8   68#628  6R8+!      =⇒= 6'M7O578   %    ! "# 0(  "  LM5    "P#:#7&        =       68 - S SS 2   == TL:P)  L=+!L:OLP628   68  628+!PMO:56."8 M    R5"  LM5!  LM#L5)    )  +    ":  P   H Q 4 Q  == ?  7    "  MP  5:#  = L7M O26  '  %  8%  = LM5 ;69%    = 0UV   '  %    "  0UV8 1           ! "#$ ?  LN#5N  )         L#5$  MP    2  Q  =⇒==    &   & & 6'8 2  Q  N N =⇒===    &     & & 6'8 ⇒ = M:5 O= :7M F= M75 O6'8 QQ ==⇒  && 6'8   %    ! "#$ ?  #>  )         7#5$  LM L  .'  <  %  7+  "  L:5     +  M7P   <A5B Q E F B C A M D M A B C C' E F A' M A B C E F N P          =⇒=⇒= Q Q   Q2 2  ==⇒===⇒    &&     & & 6'8 M    Q 5"  LM5   L-    .%      %    LM:P4L5>@<  &  M>&    L3  "  LM5  W5   "!&    "5#W#:&     1           ! "# -  %    )  LP7@9  TLM5OTPL7 68 SS  =⇒ I SSS KI =++⇒ ' =+!R  "7#L#3&     68   T:M5OTML768  ⊥⇒=⇒ SS 628         ⊥ 6R8   68#628  6R8+!:5#73#M>      "  M75     *+  !  )"  "  M75M>&  L3  W+W  !  )"   "  M75=+!5#:#W&    6."8   %     ! "# -   %    )   LM5 ?    9         "      :5     LM#            (  ) )  (   == 4  ==⇒ (     ( ) )      3+  "5#W#:&    6."8 X1     D<  )  '  <  +  7+#)  .   %  "!"  "  2!R  ":#W#5 &  "!  #  "    &  "!.)  (  '      %      '   %    )  LM5 2D  ++$(      &  "&    +(  #%                    .          !   *  +*  ,-  ./    *0    +*  -   *#1  *#$0  +*23  ,-  04  '  +*     5"  *+  *  +$   *  %/  -$6!  *  +7  "  204  8  $96 8 :   04  3  ;;-4  *      /  -3  ,,-  !   !04  4  ,,,9$0  +*23  ,-  6  5"  *+  *  +$ <    +          "! <A5B H A O B C F E Q M P H K O A B C F E Q P N H X+!Q%  '  !    %        &  "#      "   +  .        &  7+    !(  +  )  +%  &  &    (  !  )  #  *  #    %    +(  <  +  7+        %    3  +  .  )  '              M    H6  .%          !(    RY28 ?    W  "    ")  %  &  "!"  LM5LW&  M5  7#MW&  L5   #  5W  &    LM      >  5    "  !&       !                                ) ) ) ) ) )    .         !%      "W 1          <  <=*<2>#      && &   & & )) ) ) ) = + ⇒= 68 7&     ) ) & && ) )) = + 628   68  628   ) ) & & ) )   = 6R8        ) ) & & ) )   = 6Q8  ) ) & & ) )   = 6H8 )6R8#6Q8  6H8          =                   ) ) ) ) ) ) E)  +  ) ) ) ) ) )   =                    .        !%      "W   %    ! "# L  .'  <  %  7+)      "  L75    +  MW4"   M5    +  LW74"  M>5    +  LW7      =+ =⇒=+ =+     ) )   ) ) ) )       ) ) ) )         ) ) E)  +  ) ) ) ) ) )   =                    .        !%      "W X1     DE    '  %    '  %  +  *(          .K )  '            &    68#628  6R8    ''   ;M             %  )    !  %     ) ) ) ) ) ) 44 "      %  (  '    7+ <A5B Y O A B C M N P 2D  .(     +    !&  7            &  %     )    +!  %   )    &    +  7+6%  )+    8      (  .  )    .    '    +  7+    U     "   !*      +  "  %          &  ""  %   +  %    )  '    +  7+                      "  )  +%  %  !              ("    +   #  ("  )    )  .'      #             <      +       $              )  .&  " F)  .)  '  <  +  7+ F9          .        "   M    Y5%  LM5-  ?  G  #G 2 )        %    !       ."  LM5  LM-5  "     22 2 2  Q ?? =+  1     ?    !!      LM&  L5  W 2 #&   M-  W  +!W     W 2    )"  !       ."  LM-  LM5  W  LO G  4W 2 MOG 2    (    ! "# ()  ∆ )   ? ) (  ) ) 2  =⇒=⇒∆ () 2 ∆ )   ? ) (  ) ) 2 22 =⇒=⇒∆ 22 2 2  2 2 2  Q22 Q 86Q ???? )) =+⇒         +=+⇒  6E  +  WL 2 FWM 2  O 2 8 <  )+      '    #  "    +  %   3  +&  )    !&            !&    +  7+ ;E     ''   %  "!       %    ! "# L  .'  <  +  7+  "  LMW    +  9W 2 W        2 2   2 2 = − − ⇒= ? )? ?) ? ) )) )) ) ( ( ) ) ) ? ) )? ?) )? ? ? −= − = − − =⇒  2  2  22 68 7&      +  M9WW    L9W 2 W            .   )?  )?  2  2 2  == 628   68  628 22 2 2   2 2 2 2  Q Q ?? ? ?  ?? ? ? =+⇒−=⇒ 6."8 • 1     DM    !         6  8!   6%  '  *"    '  8  &  7  +)  +  +              %    #      )#  .    %   <A5B J O1 a O2 B D C A O K   '  #    .                    .  <  %  7 +F-  +%    &  F3      !  !  E)  +  )  .  "    C  C            ; 2D>        "        Y+*    µ 0 A 60= ,'!  20   +  +*  -    **  .04  2  )1?#$@  *?  -  ? % !  !04  !  7  /   04  2    **  .  +*  ')-  )$0  +*23   2 2 2 1 2 1 1 4 R R R + = $ 1    &  &   <  &  W3&  LM#L5)      7  .)       L&    !  6W8  - F -    "  M3W5       .   #      + ! · · 0 MHB OCB 30= = ⇒ AMN ∆    7&     · · · · 0 0 OAC (180 AOC) : 2 90 ABC MAH= − = − = ⇒ AMH ANO ∆ = ∆ 68  ⇒ L3OLW  ⇒ L3-W  %    FL  .'      Y  + 2 2 2 1 2 1 1 4 R R R + =  M    J6<  &  ="=8 5"  LM5    .!  !  6W8<  "7    !  6W8?   LN#MN#5N)      %         7$  M5#5L#LM5  " !&  LN#MN#5N  "    &  6<  &            &   ="=8 1       (    ! "# F  7!    "  %    TLM5  ." F  7    M56   L8 =  '        LM75#MLN75N#5MNLN7    .      SSSS NNN4NNN  ==  7   SSS I SSS NNKINN  ++==++    SS NN  = SS NNNN  =⇒ -M#LN# 5&    5N#LN#MN&    6."8 • 1     D0        %  !&  (        !&    +  7 +  ;5        '    +  7+         ;     $&   <A5B K O B C A M A' C' B' N M O H D C B A +#("    %    "  )      !    "         M)+            !&  7+<)+  )      %            6%  ).              &  7  +8# "  %    )  .  #)  .     '    #  .  .)%     +  (          &  7+)  )  +#!%              0                 %    ! "# 3  +  +    &  ."    '  T7LN5  T 75NL4T7MLN T7LMN4T75NM T7MN5        N N  N N  N N  N N  N N  N N N N 4 N N 4 N N =⇒=⇒===                         (  +      7+  LN#MN#5N&    6."8 2DE  *(%                # ,"  LM5      7+  !  M5   L%  7M  75+  /9         5"  LM5    .  !  6W8  7  "    "'  !   M5     "L3  L:#LP)         7M#755  " :P *"    "    6(  *        !%    "      )      L$  M5M        "8 X  "  #    +    +  +        &  !"%  )  )     "     A  *    "    *  *73    ! "04  B3     *  *73    ! "04  2  */      *  *73  /        "04   04  BA6X8M&"       %  ")  +      *         J#))+$           M    K5"  LM5%  ")  .  .    "7!"&  .&   %      7R    "    R  "&     1     ?  7    "  )  .  .6=8.  %  "  5N#LN#MN(      %      7 LM#M5#5L6$("%  !8   7 ∈ 6=8 ⇔ LN#MN#5N&     ⇔ S 2 S  NN  =  I SSSSSS KINNNN =+⇔=⇔=⇔  ⇔     LM75    .  ⇔ 7     !      .TLM5    )  .J  K(        )  .     M    Z6<  "7*(8M    &  &     Y  "    Q"  5  " <A5B Z I M E B A C D F J K L !&      !      .Q"    +  "    "6<  "          "7*(8 1     ?    Q  &   "  &      Q"  6$("%  (  8?  7    "  :      !      .TL-:  T5:P5  7$       L-#L:#-:#5P(      #[#9  1 (  J  #[#9&     [#9#1&     ⇒ #[#9#1&     (    K+!7  &  "!    !      .TLMP  T 5M-E)  +    !      .Q"  L-:#5P:#LMP  5M-  *+     "7 M    I5"    LM55    LLN#MMN  55N&    W <  &  '*W    L5&  LNMN  MN5N)      7#5   "W7OW 1     <    !          *(   M      04  C,C,C  +*  !  D04  .*  2       C,C,C  +*  CCC$CCC  *!  +*  20  +#$ 5  " F    "   %  TLNMN5N+       &  #  ." F    "     5  =  '        .K  "*"     '         SS NNNN )) =  ⇒ ." 6    "$      8 5  2=  '        .Z          .#6$(" %  (  8  WLN5MN  WMNL5N            .    SSSS NNN4NNN )))) == 7   SS NN )) =   SS NNNN )) =     ." F"      "   L  .'  M        .  7  L5MNW            .)  #)  +  W7OW6."8 )  $(  !&      &  'N  *W    LM#&  MN5N  5NLN)      :#P%        W:OWPE)  +       <A5B I d M N O A B C A' B' C' [...]... công trong ho ̣c tâ ̣p ́ VII- NHỮ NG KIÊN NGHI : ̣ Cách da ̣y, cách ho ̣c truyề n thu ̣ mô ̣t chiề u tồ n ta ̣i đã khá lâu trong nhà trường từ THCS đế n THPT, la ̣i bi ̣na ̣n “da ̣y thêm, ho ̣c thêm tràn lan làm cho năng lưc tự ho ̣c bi ̣ ̣ thoái hóa ngày càng trầ m tro ̣ng hơn Do vâ ̣y tôi xin đề nghi ̣ các cơ quan, ban ngành đoàn thể quan tâm đế n các vấ n đề sau: +... làm đươ ̣c mà phải kế t hơ ̣p với toàn bô ̣ giáo viên có nhiê ̣t huyế t về toán ) Nhưng các ba ̣n cứ tâ ̣p suy nghi ̃ như thế đi, các ba ̣n sẽ nhâ ̣n thấ y nhiề u điề u mới la ̣, tăng thêm trí suy luâ ̣n, nâng cao nhâ ̣n thức về tư duy trừu tươ ̣ng, rèn luyê ̣n tố t ki ̃ năng, ki ̃ xảo Đó cũng là bước đầ u để các ba ̣n tâ ̣p làm quen với tìm tòi nghiên cứu sau này... 1 0 0 ́ ̀ VI/ LƠI KÊT Nế u các ba ̣n đã ho ̣c đinh lý Mê-nê-la-uyt và đo ̣c bài viế t này rồ i tôi nghi ̃ ba ̣n có ̣ thể giải các bài toán hình ho ̣c go ̣n hơn rấ t nhiề u Cầ n nói thêm rằ ng phương pháp dùng Mê-nê-la-uyt mà ta nghiên cứu trên kia không phải lúc nào cũng thực hiê ̣n đươ ̣c ( chỉ thực hiê ̣n đươ ̣c mô ̣t chiề u ) và không thí điể m rô ̣ng rai ( không... và ho ̣c Phải từ quan hê ̣ “thầ y giảng, trò chép” thu ̣ đô ̣ng chuyể n sang quan hê ̣ “thầ y hướng dẫn, trò nỗ lực thực hành đế n mức cao nhấ t” Đẩ y lùi những tiêu cực như ho ̣c thêm, ho ̣c tủ, gian lâ ̣n trong thi cử… + Phát huy năng lưc tự ho ̣c, tự nghiên cứu của giáo viên hằ ng năm thông qua các ̣ hô ̣i thảo về toán ho ̣c, viế t chuyên đề , viế t sáng kiế... dựng quy trình tự ho ̣c ( làm thí điể m ở vài lớp ) tiế n đế n phong trào tự ho ̣c trong toàn ho ̣c sinh + Đổ i mới nô ̣i dung thi cử (nhấ t là kì thi ho ̣c sinh giỏi cấ p huyê n), làm cho thi cử không còn chỉ là kiể m tra trí nhớ, thách đố bằ ng những bài toán lắ c léo mà thử thách năng lực nắ m bản chấ t vấ n đề , năng lực tư duy, năng lưc phát hiê