ความเท่ากันทุกประการ

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ความเท่ากันทุกประการ

  1. 1. 5 ( 1 2 A B A B C D 1
  2. 2. AB CD AB = CD A B C D AB CD A C AB =CD B D AB CD AB = CD AB  CD ˆ AOB ˆ CED  ˆ   ˆ m AOB  m CED  A C   O E B D ˆ AOB ˆ CED O E 2
  3. 3. OA EC  ˆ   ˆ m AOB  m CED  OB ED ˆ AOB ˆ CED  ˆ   ˆ m AOB  m CED  ˆ AOB  ˆ CED 5 ( 1 2 3
  4. 4.  MNL   STU 1) c – e = ……………………….. 2) ˆ ˆ L T = ……………………….. 3) b + c = ……………………….. 4) ˆ ˆ M N = ……………………….. 5) a : b : c = ……………………….. ................................... ....................................................................................... ..... ............ .............. 4
  5. 5. 5 ( - 1 2 1. . . . . 2. . . . . 5
  6. 6. 3. . . . . 4. . . . . 5. 60 . . . . ....................................................................................... ..... ............ .............. 5 ( 2 2 6
  7. 7. ABC DEF A D AB = DE, BC = EF CA = FD ˆ ˆ ˆ ˆ A  D, B  E ˆ ˆ CF ABC DEF AB = DE, BC = EF CA = FD ˆ ˆ ˆ ˆ A  D, B  E ˆ ˆ CF  ABC  DEF  ABC   DEF 7
  8. 8. ABC DEF ˆ ˆ AD AB = DE ˆ ˆ BE BC = EF ˆ ˆ CF CA = FD  ABC   DEF 8
  9. 9. 5 ( 2 2  ABD   BCD  BCD   BCE C 9
  10. 10. A E B ………….1 ABCD = BECD ………….2  ABD   BCE ………….3 ˆ ˆ DAB  CEB ………….4 AD + CD – CE = AB + BC - BE ....................................................................................... ..... ............ .............. 5 10
  11. 11. ( - 2 2 11
  12. 12. ....................................................................................... ..... ............ .............. 5 ( 3 2 “ ” 12
  13. 13. AB CD O AO = BO CO = DO AOC  BOD AB CD O AO = BO CO = DO AOC  BOD AOC BOD AO = BO ˆ ˆ AOC  BOD ---- CO = DO AOC  BOD 5 ( 3 2 13
  14. 14. ABCD E F AB BC DE DF D C F A B E ……………………………………………………………………… ……………………………………………………………………… … ……………………………………………………………………… ……………………………………………………………………… … ……………………………………………………………………… ……………………………………………………………………… … ……………………………………………………………………… ……………………………………………………………………… … ……………………………………………………………………… ……………………………………………………………………… … 14
  15. 15. ……………………………………………………………………… ……………………………………………………………………… … ……………………………………………………………………… ……………………………………………………………………… … ……………………………………………………………………… ……………………………………………………………………… … ……………………………………………………………………… ……………………………………………………………………… … ....................................................................................... ..... ............ .............. 5 15
  16. 16. ( - 3 2 -- 1. - - . . . . 2–3 2. A ABC BD = CE ABD =  ACE . - - . - - . - - . 3. . AD = AE . ADE . ˆ ˆ ADE  AED . 4. “ ” -- 16
  17. 17. .  .  .  .  5. . . . . 1 ....................................................................................... ..... ............ .............. 5 ( 4 2 - - . . . – – ( . . .) 17
  18. 18.    MX CX ,CN MN AX = AN MAX   CAN ˆ ˆ AMX  ACN    MX CX ,CN MN AX = AN MAX   CAN ˆ ˆ AMX  ACN MAX  CAN AXM  ANC  90 ( ˆ ˆ    ) MX CX ,CN MN AX = AN ( ) ˆ ˆ MAX  CAN ( ) ˆ ˆ AMX  ACN ( . . .) ˆ ˆ AMX  ACN ( ) 5 ( 18
  19. 19. 4 2 - - DE = DF , ˆ ˆ DEC  DFB BE = CE ……………………………………………………………………… ……………………………………………………………………… … ……………………………………………………………………… ……………………………………………………………………… … ……………………………………………………………………… ……………………………………………………………………… … ……………………………………………………………………… ……………………………………………………………………… … 19
  20. 20. ……………………………………………………………………… ……………………………………………………………………… … ……………………………………………………………………… ……………………………………………………………………… … ……………………………………………………………………… ……………………………………………………………………… … ……………………………………………………………………… ……………………………………………………………………… … ……………………………………………………………………… ……………………………………………………………………… … 20
  21. 21. ....................................................................................... ..... ............ .............. 5 ( - 4 2 - - 1. PO = OS PQO = RSO - - . OPQ = OSR . PQO = ROS . OPQ = ORS . POQ = OSR 2.  ABC =  DEF - - . BC = EF . AB = DE . AC = DF . ABC = DEF 3. ABC = ABD ABC = ABD - - 21
  22. 22. . AC = AD . BC = BD . ACB = ADB . BAC = BAD 4. . 90 . . . 5. . . . . ....................................................................................... ..... ............ .............. 5 ( 5 2 - - 22
  23. 23. – – – – ( . . )  SEA  TEA SE = TE SA = TA  SEA   TEA ˆ ˆ SAE  TAE  SEA  TEA SE = TE SA = TA  SEA   TEA ˆ ˆ SAE  TAE  SEA  TEA SE = TE ( ) SA = TA ( ) EA = EA ( EA )  SEA   TEA ( . . ) ˆ ˆ SAE  TAE ( ) 23
  24. 24. 5 ( 5 2 - - ……………………………………………………………………… ……………………………………………………………………… … ……………………………………………………………………… ……………………………………………………………………… … 24
  25. 25. ……………………………………………………………………… ……………………………………………………………………… … ……………………………………………………………………… ……………………………………………………………………… … ……………………………………………………………………… ……………………………………………………………………… … ……………………………………………………………………… ……………………………………………………………………… … ……………………………………………………………………… ……………………………………………………………………… … ……………………………………………………………………… ……………………………………………………………………… … ……………………………………………………………………… ……………………………………………………………………… … 25
  26. 26. ....................................................................................... ..... ............ .............. 5 ( - 5 2 - - 1. AC =AD ABC = ABD - - . AB = AC . ACB = ADB . BC = BD . AB = AC 2. - - 26
  27. 27. . 3. - - . . . . 4. ABC = DBC D A . - - B . - - C . - - . 5. “ ” .  .  .  .  ....................................................................................... ..... ............ .............. 27

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