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# Cours1

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### Cours1

1. 1. ‫ال ّرس 3: المثّثات المتقايسة‬ ‫ل‬ ‫د‬ 1 ‫1 المثّثات المتقايسة ال ّوايا‬ ‫ز‬ ‫ل‬ A F G AC  BC AB  BC   AC  E E AD  BC ABC 1 2 AEF FGC G E F 3 E AC  FGC ABCD  E AEF 2 ‫حاالت تقايش المثّثات العا ّة‬ ‫م‬ ‫ل‬ E F 2 A G C B EFG ABC
2. 2. E F BC AB  AC  A I ABC  AB  BC  I I ˆ ˆ AIF  ICE 1 ˆ CIE  90 IAF AC  BI  D 2 CIE ABC I BC  A ˆ ˆ IAD  ICB ˆ ˆ AID  BIC IAD 1 2 IBC 3 4 3 G A E F B C EFG ABC ABCD AE  B ˆ ˆ DAB  CBE E 1 ABD 2 BEC
3. 3. 3 ABCD BC AI  JC JCD J AD  AIB I 1 2 IBJD 3 4 G A E B F C EFG ABC AB    BCD D C ACD 1 2 AB  4 2 A C 3 B C' N ANB M AMB C' C 1
4. 4. AB  ˆ MA N 2 5 ABCD AC  AM  CN M N ABM ˆ ˆ BMN  MND NCD 1 2 ND BM  ABCD AD  AC  BC  EO  E F OFC O 1 AEO EF  O 2 6 ‫حاالت تقايش المثّثات القائمة‬ ‫ل‬ 3 C G E F A B EFG ABC ABCD BC   AD  ˆ ˆ ABE  FDC A C E F 1
5. 5. ABE 2 CFD 3 ABCD A AM  CN  ABD C CBD ˆ ˆ ABM  NDC 1 ABM CND 2 7 C G E F A B EFG ABC C O ˆ AOB M B ' C B A MBO MAO A  C 1 2 A E C  AC  B ACE ABC  AB  ABE 1 2 8
6. 6. ‫المثّثات المتقايسة ال ّلعين‬ ‫ض‬ ‫ل‬ A 4 ABC BC I ABI AIC 1 A C B ˆ ACB ˆ ABC A ABC BC AB  AC  I E I F I IEB IFC 1 AE  AF 2 ABCD DC  BE  DF ADF F ABE BC E 1 CEF 2 EF   AC  3 9 A ABC
7. 7. BC I BC AIB AIC Ax  ˆ BAC 1  AI  2 2 A ABC AC  AB  EF   AI  AE  AF BC F E I 1 ˆ ˆ EAI  IAF BC  AI  EF //BC  2 10 ˆ ˆ ABC  ACB BC I ABC ˆ BAC ˆ ˆ AIB  AIC AIC 1 AIB 2 ABCD AD  AE  DF ˆ ˆ AEB  DFC IEF F CF  BE  I IBC E 1 2 3 A ABC I BC ˆ BAC
8. 8.  AI   BC  E  AB  1 BC   AI  //CE  C 2 ABC 11 ‫المثّثات المتقايسة األضالع‬ ‫ل‬ 5 60 60 ABC B A E A C F AEF 12 ‫من ّف زاوية‬ ‫ص‬ ˆ xAy M Ay  Ax  M K AMK AMH y K z M A H x 6 H
9. 9. MK MH ABC ˆ ACB I  AC   AB  BC  ˆ ABC I G F E IE  IF  IG y K z M A H x Ay  Ax  M A ABC M ABC BF  CE  ˆ ˆ FBC  ECB FB EC ME  MF ˆ BAC AM  1 M 2