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هندسة للصف الاول الاعدادى الترم الاول 2017 - موقع ملزمتي

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هندسة للصف الاول الاعدادى الترم الاول 2017 - موقع ملزمتي

  1. 1. ‫اﻟﺨﻮا‬‫ر‬‫اﻟ‬ ‫ﻓﻰ‬ ‫زﻣﻰ‬‫ﻬﻨﺪﺳﺔ‬‫اﻹﻋﺪادى‬ ‫اﻷول‬ ‫اﻟﺼﻒ‬ ‫أ‬/‫ﻣﺤﻤﻮد‬ ‫ﻣﺤﻤﺪ‬‫ت‬/٠١٢١١١٦٥٠١٢ 
  2. 2. ‫اﻟﺨﻮا‬‫ر‬‫اﻟ‬ ‫ﻓﻰ‬ ‫زﻣﻰ‬‫ﻬﻨﺪﺳﺔ‬‫اﻹﻋﺪادى‬ ‫اﻷول‬ ‫اﻟﺼﻒ‬ ‫أ‬/‫ﻣﺤﻤﻮد‬ ‫ﻣﺤﻤﺪ‬‫ت‬/٠١٢١١١٦٥٠١٢   ‫ﻣ‬‫ﻫﻨﺪﺳﻴﺔ‬ ‫ﻔﺎﻫﻴﻢ‬    ‫ﺍﻟﺘﻄﺎﺑﻖ‬    ‫ﺍﻟﻤﺜﻠﺜﺎﺕ‬ ‫ﺗﻄﺎﺑﻖ‬   ‫ﺍﻟﺘﻮﺍﺯﻱ‬    ‫ﺍﻟﻬﻨﺪﺳﻴﺔ‬ ‫ﺍﻷﻧﺸﺎﺀﺍﺕ‬   
  3. 3. ‫اﻟﺨﻮا‬‫ر‬‫اﻟ‬ ‫ﻓﻰ‬ ‫زﻣﻰ‬‫ﻬﻨﺪﺳﺔ‬‫اﻹﻋﺪادى‬ ‫اﻷول‬ ‫اﻟﺼﻒ‬ ‫أ‬/‫ﻣﺤﻤﻮد‬ ‫ﻣﺤﻤﺪ‬‫ت‬/٠١٢١١١٦٥٠١٢  ‫ﺍﻷﻭﻝ‬ ‫ﺍﻟﺪﺭﺱ‬       )(:-                  )(:-              )(:-              )(:-            – ‫ﻫﻨﺪﺳﻴﺔ‬ ‫ﻣﻔﺎﻫﻴﻢ‬  hf.hf=hf=٤‫ﺳﻢ‬ hf،hf hfhfhf ):hf≠hf( h‫ب‬ ٤‫ﺳﻢ‬     hf  :-hf‫ﺥ‬hfhf  )( hf.hf≠fh )hf‫ﺥ‬hf‫ﺥ‬hf(   ‫ﺲ‬‫ﺳ‬،‫ﺹ‬،....... ):-hf‫ﺲ‬‫ﺳ‬ ‫ﺥ‬( )hf‫ﺥ‬hf‫ﺥ‬hf( ‫أ‬ ‫ب‬ ‫ﺳ‬ h ‫ب‬ hf
  4. 4. ‫اﻟﺨﻮا‬‫ر‬‫اﻟ‬ ‫ﻓﻰ‬ ‫زﻣﻰ‬‫ﻬﻨﺪﺳﺔ‬‫اﻹﻋﺪادى‬ ‫اﻷول‬ ‫اﻟﺼﻒ‬ ‫أ‬/‫ﻣﺤﻤﻮد‬ ‫ﻣﺤﻤﺪ‬‫ت‬/٠١٢١١١٦٥٠١٢  )(:-                  ‫ﺍﻟﺰﺍﻭﻳﺔ‬ ‫ﻗﻴﺎﺱ‬:-   )٥ (،)/ (،)// ( ١٥ =٦٠/ ،١/ =٦٠// )hfO(≠R)hfO( )hfO(fh،fO. R)hfO(. ‫ﺍﻟﺰﻭﺍﻳﺎ‬ ‫ﺃﻧﻮﺍﻉ‬:-‫ﻫﻲ‬ ‫ﺃﻧﻮﺍﻉ‬ ‫ﻋﺪﺓ‬ ‫ﺇﱃ‬ ‫ﺎ‬‫ﻗﻴﺎﺳﺎ‬ ‫ﲝﺴﺐ‬ ‫ﺍﻟﺰﻭﺍﻳﺎ‬ ‫ﺗﻨﻘﺴﻢ‬: ‫ﺍﻟﺰﺍﻭﻳﺔ‬‫ﻗﻴﺎﺳﻬﺎ‬‫ﺭﲰﻬﺎ‬ ‫ﺯﺍﻭﻳﺔ‬‫ﺻﻔﺮﻳﺔ‬ =٥  ‫ﺯﺍﻭﻳﺔ‬‫ﺣﺎﺩﺓ‬   ‫ﺻﻔﺮ‬٥ ٩٠٥ ‫ﺯﺍﻭﻳﺔ‬‫ﻗﺎﺋﻤﺔ‬ =٥ ٩٠=٦٠/ ٨٩٥ =٦٠// ٥٩/ ٨٩٥ ‫ﺯﺍﻭﻳﺔ‬‫ﻣﻨﻔﺮﺟﺔ‬ ٩٠٥  ١٨٠٥ ‫ﺯﺍﻭﻳﺔ‬‫ﻣﺴﺘﻘﻴﻤﺔ‬ =٥ ١٨٠=٦٠/ ١٧٩٥ =٦٠// ٥٩/ ١٧٩٥ ‫ﺯﺍﻭﻳﺔ‬‫ﻣﻨﻌﻜﺴ‬‫ﺔ‬ ١٨٠٥  ٣٦٠٥ . f      )‫ب‬hO(،)Ohf(،)h( fhhO ‫ﺯ‬ ‫ﺯ‬ ‫ﺯ‬ ‫ﺯ‬ ‫ﺯ‬ ‫ﺯ‬ ‫ﺯ‬ O f hO f h f h f O f hO h f O O h ■ h ‫ﺿﻠﻊ‬ ‫ﺿﻠﻊ‬ ‫رأس‬ f O
  5. 5. ‫اﻟﺨﻮا‬‫ر‬‫اﻟ‬ ‫ﻓﻰ‬ ‫زﻣﻰ‬‫ﻬﻨﺪﺳﺔ‬‫اﻹﻋﺪادى‬ ‫اﻷول‬ ‫اﻟﺼﻒ‬ ‫أ‬/‫ﻣﺤﻤﻮد‬ ‫ﻣﺤﻤﺪ‬‫ت‬/٠١٢١١١٦٥٠١٢   ‫ﻣﻼﺣﻈﺔ‬:- ٣٦٠٥ ‫ﻣﺜﺎﻝ‬:R)hfO(=١٢٠٥ :R)hfO(=٣٦٠٥ ‫ـ‬‫ــ‬١٢٠٥ =٢٤٠٥ )١(‫اﻻﺗﻰ‬ ‫اﻟﺠﺪول‬ ‫اﻛﻤﻞ‬:- R)hfO(٤٥٥ ١٨٠٥ ٢٠٠٥ ١٥٠٥ ٩٠٥ ٦٠/ ١٧٩٥ ‫ﻧﻮﻋﻬﺎ‬ )٢(‫اﻻﺗﻰ‬ ‫اﻟﺠﺪول‬ ‫اﻛﻤﻞ‬:- R)hfO(١٣٥٥ ٥٨٥ ٨٠٥ ١٠٠٥ ١١٠٥ ٩٠٥ R)hfO(‫ﺍﳌﻨﻌﻜﺴﺔ‬  )(‫ﺍﳌﺘﺠﺎﻭﺭﺗﺎﻥ‬ ‫ﺍﻟﺰﺍﻭﻳﺘﺎﻥ‬:-  ‫ﺍﳌﻘﺎﺑﻞ‬ ‫ﺍﻟﺸﻜﻞ‬ ‫ﻓﻰ‬:- )hfx(،)xfO(:- ffx fh،fOfx   ‫ﺍﳌﻘﺎﺑﻞ‬ ‫ﺍﻟﺸﻜﻞ‬ ‫ﻓﻰ‬: )١()hfx(،)xfO( fO،fh‫ب‬x ‫ﺍﳌﻘﺎﺑﻞ‬ ‫ﺍﻟﺸﻜﻞ‬ ‫ﰲ‬: )٢()hfO(،)Oxi(   ‫ﺯ‬ ‫ﺯ‬ ‫ﺯ‬ ‫ﺯ‬ ‫ﺯ‬ ‫ﺍﻟﺰﻭﺍﻳﺎ‬ ‫ﺑﲔ‬ ‫ﺍﻟﻌﻼﻗﺎﺕ‬ ‫ﺑﻌﺾ‬   h xO f ‫ﺯ‬‫ﺯ‬ ‫ﻫﺎﻣﺔ‬ ‫ﻣﻼﺣﻈﺎﺕ‬ ‫ﺯ‬ ‫ﺯ‬ h f O x ‫ﺯ‬‫ﺯ‬ hf i O x
  6. 6. ‫اﻟﺨﻮا‬‫ر‬‫اﻟ‬ ‫ﻓﻰ‬ ‫زﻣﻰ‬‫ﻬﻨﺪﺳﺔ‬‫اﻹﻋﺪادى‬ ‫اﻷول‬ ‫اﻟﺼﻒ‬ ‫أ‬/‫ﻣﺤﻤﻮد‬ ‫ﻣﺤﻤﺪ‬‫ت‬/٠١٢١١١٦٥٠١٢    )(‫ﺍﳌﺘ‬ ‫ﺍﻟﺰﺍﻭﻳﺘﺎﻥ‬‫ﺘﺎﻣﺘﺎﻥ‬:-  َ‫ﻼ‬‫ﻓﻤﺜ‬:٣٠°،٦٠°:٣٠°+٦٠°=٩٠° )(‫ﺍﳌﺘ‬ ‫ﺍﻟﺰﺍﻭﻳﺘﺎﻥ‬‫ﻜﺎﻣﻠﺘﺎﻥ‬:-  َ‫ﻼ‬‫ﻓﻤﺜ‬:١٢٥°،٥٥°:١٢٥°+٥٥°=١٨٠° )(‫ﺍﻟﺰﺍﻭﻳﺘﺎﻥ‬‫ﺍﳌﺘﺠﺎﻭﺭﺗﺎﻥ‬‫ﺍﳌﺘ‬‫ﻜﺎﻣﻠﺘﺎﻥ‬:-      =°    Y                                                        Y                                                           Y                   )                        (                    َ‫ﻼ‬‫ﻓﻤﺜ‬:‫ﻛﺎن‬ ‫إذا‬: )f( )h(‫ﻓﺈن‬:R)‫ب‬(=R)O( )O( ‫ﺯ‬ ‫ﺯ‬ ‫ﺯ‬ ‫ﺯ‬ ‫ﺯ‬ ‫ﺗﺘﻤﻢ‬ ‫ﺗﺘﻤﻢ‬ =°    Y                                               Y                                                                Y                  )                        (                    َ‫ﻼ‬‫ﻓﻤﺜ‬:‫ﻛﺎن‬ ‫إذا‬: )f( )h(‫ﻓﺈن‬:R)‫ب‬(=R)O( )O( ‫ﺗﻜﻤﻞ‬ ‫ﺗﻜﻤﻞ‬ ‫ﺯ‬‫ﺯ‬ ‫ﺯ‬ ‫ﺯ‬ ‫ﺯ‬  =° 
  7. 7. ‫اﻟﺨﻮا‬‫ر‬‫اﻟ‬ ‫ﻓﻰ‬ ‫زﻣﻰ‬‫ﻬﻨﺪﺳﺔ‬‫اﻹﻋﺪادى‬ ‫اﻷول‬ ‫اﻟﺼﻒ‬ ‫أ‬/‫ﻣﺤﻤﻮد‬ ‫ﻣﺤﻤﺪ‬‫ت‬/٠١٢١١١٦٥٠١٢  )(‫ﺍﻟﺰﺍﻭﻳﺘﺎﻧ‬‫ﺑﺎﻟﺮﺃﺱ‬ ‫ﺎﳌﺘﻘﺎﺑﻠﺘﺎﻥ‬:-    h‫ب‬∩Ox=}‫م‬{ :R)h‫م‬x(=R)O‫ب‬ ‫م‬(. ،R)h‫م‬O(=R)x‫م‬f(. )(‫ﻧﻘﻄﺔ‬ ‫ﺣﻮﻝ‬ ‫ﺍﳌﺘﺠﻤﻌﺔ‬ ‫ﺍﻟﺰﺍﻭﻳﺎ‬:-  )١(‫ﻓﻤﺜﻼ‬َ:‫ﺍﳌﻘﺎﺑﻞ‬ ‫ﺍﻟﺸﻜﻞ‬ ‫ﻓﻰ‬: :R)‫ب‬hx(=٣٥°،R)xhi(=١٠٠° ،R)ihO(=٤٥° ‫ﻓﺈﻥ‬:R)‫ب‬hx(+R)xhi(+R)Ohi( =٣٥°+١٠٠°+٤٥°=١٨٠° Eh‫ب‬،hO.   ‫ﺯ‬‫ﺯ‬ ‫ﺯ‬ ‫ﺯ‬‫م‬ ● hx f O ● XX =°  ‫ﻣﺘﺠﺎﻭﺭﺗﲔ‬ ‫ﻟﺰﺍﻭﻳﺘﲔ‬ ‫ﺍﳌﺘﻄﺮﻓﺎﻥ‬ ‫ﺍﻟﻀﻠﻌﺎﻥ‬ )=°(     )≠°(   ‫ﺯ‬ ‫ﺯ‬ ‫ﺯ‬ ‫ﺯ‬ ‫ﺯ‬ ‫ﺯ‬ ٣٥ ٥ fhO x ٤٥ ٥ i ١٠٠ ٥
  8. 8. ‫اﻟﺨﻮا‬‫ر‬‫اﻟ‬ ‫ﻓﻰ‬ ‫زﻣﻰ‬‫ﻬﻨﺪﺳﺔ‬‫اﻹﻋﺪادى‬ ‫اﻷول‬ ‫اﻟﺼﻒ‬ ‫أ‬/‫ﻣﺤﻤﻮد‬ ‫ﻣﺤﻤﺪ‬‫ت‬/٠١٢١١١٦٥٠١٢  )٢(‫ﺍﳌﻘﺎﺑﻞ‬ ‫ﺍﻟﺸﻜﻞ‬ ‫ﻓﻰ‬: ‫ﻫﻞ‬Oh،O‫ب‬‫ﻻ‬ ‫ﺃﻡ‬ ‫ﻭﺍﺣﺪﺓ‬ ‫ﺇﺳﺘﻘﺎﻣﺔ‬ ‫ﻋﻠﻲ‬،‫؟‬ ‫ﻭﳌﺎﺫﺍ‬ eR)h‫ب‬x+ (R)x‫ب‬O= (٧٠+١٠٠ =١٧٠°≠°. E‫ب‬h،‫ب‬O. ‫ﹶ‬‫ﻼ‬‫ﻓﻤﺜ‬:‫ﺍﳌﻘﺎﺑﻞ‬ ‫ﺍﻟﺸﻜﻞ‬ ‫ﻓﻰ‬: :R)h‫ب‬ ‫م‬(=٣٠°،R)‫ب‬‫م‬O(=٦٠° ‫ﻓﺈﻥ‬:R)h‫ب‬ ‫م‬(+R)‫ب‬‫م‬O( =٣٠°+٦٠°=٩٠° E)h‫م‬O(‫ﻗﺎﺋﻤﺔ‬ ‫ﺯﺍﻭﻳﺔ‬. E‫م‬hn‫م‬O. ‫ﺍﳌﻘﺎﺑﻞ‬ ‫ﺍﻟﺸﻜﻞ‬ ‫ﻓﻔﻲ‬: fx)hfO( R)hfx(=R)xfO= (R)hfO( fx)hfO( ‫ﺯ‬‫ﺯ‬١٠٠٥ h ٧٠٥ ‫ب‬ O x ‫ﺯ‬‫ﺯ‬ ‫ﺯ‬‫ﺯ‬ ‫ﺯ‬‫م‬ O h f ٦٠٥ ٣٠٥ ١ ٢ ‫ﺯ‬ ‫ﺯ‬ ‫ﺯ‬ ‫ﺯ‬ ‫ﺯ‬ ‫ﺢ‬‫ﳒ‬ ‫ﺢ‬‫ﳒ‬ h‫ب‬ O x ‫ﻣﻼﺣﻈــــــــﺔ‬ )=°(  ‫ﺍﻟﺰﺍﻭﻳﺔ‬ ‫ﻣﻨﺼﻒ‬  
  9. 9. ‫اﻟﺨﻮا‬‫ر‬‫اﻟ‬ ‫ﻓﻰ‬ ‫زﻣﻰ‬‫ﻬﻨﺪﺳﺔ‬‫اﻹﻋﺪادى‬ ‫اﻷول‬ ‫اﻟﺼﻒ‬ ‫أ‬/‫ﻣﺤﻤﻮد‬ ‫ﻣﺤﻤﺪ‬‫ت‬/٠١٢١١١٦٥٠١٢  )١(‫ﺍﻻﺗﻰ‬ ‫ﺍﳉﺪﻭﻝ‬ ‫ﺍﻛﻤﻞ‬:- ‫ﺍﻟﺰﺍﻭﻳﺔ‬ ‫ﻗﻴﺎﺱ‬٧٥٥ ٩٠٥ ٢٠٥ ٤٥٥ ‫ﻣﺘﻤﻤﺘﻬﺎ‬ ‫ﻗﻴﺎﺱ‬٦٧٥ ٣٠٥ ‫ﻣﻜﻤﻠﺘﻬﺎ‬ ‫ﻗﻴﺎﺱ‬١٥٤٥ ٣٠/ ١١٥٥ )٢(‫ﺍﻟﺘﺎﻟﻴﺔ‬ ‫ﺍﻷﺷﻜﺎﻝ‬ ‫ﻣﻦ‬ ‫ﻛﻞ‬ ‫ﰲ‬: ‫ﻛﺎﻧﺖ‬ ‫ﺇﺫﺍ‬:‫م‬Jhf‫ﺑﺎﻟﻌﻼﻣﺔ‬ ‫ﺇﻟﻴﻬﺎ‬ ‫ﺍﳌﺸﺎﺭ‬ ‫ﺍﻟﺰﺍﻭﻳﺔ‬ ‫ﻗﻴﺎﺱ‬ ‫ﻓﺄﻭﺟﺪ‬)‫؟‬: ( R)x‫ب‬ ‫م‬(=...........R)x‫ب‬ ‫م‬(=...........R)x‫ب‬ ‫م‬(=........... )٣(‫ﰲ‬‫ﺍﻟﺘﺎﻟﻴﺔ‬ ‫ﺍﻷﺷﻜﺎﻝ‬ ‫ﻣﻦ‬ ‫ﻛﻞ‬: OhOf          )٤(‫ﺍﻟﺘﺎﻟﻴﺔ‬ ‫ﺍﻷﺷﻜﺎﻝ‬ ‫ﻣﻦ‬ ‫ﻛﻞ‬ ‫ﰲ‬: fhnfO            R)h‫ب‬x(=...........R)x‫ب‬O(=...........‫س‬=...........  – ‫ﺯ‬ h x ‫م‬‫ب‬ ٥٠°‫؟‬ ٣٥° ١٠٠° h x ‫م‬‫ب‬ ‫؟‬ O h x ‫م‬‫ب‬ ٤٥° ‫؟‬ ■ O ‫ﺯ‬‫ﺯ‬ * ٦٠°* h x O‫ب‬ i ١٠٨° ٦٢° x O ‫ب‬ h ٣٥° ١٠٠° h x ‫م‬‫ب‬ ‫؟‬ O ‫ب‬ O h x ٦٥٥ ‫ب‬ O h x * * * i x ‫ب‬ O h ‫س‬ ٤٠° * i ‫ﺯ‬‫ﺯ‬
  10. 10. ‫اﻟﺨﻮا‬‫ر‬‫اﻟ‬ ‫ﻓﻰ‬ ‫زﻣﻰ‬‫ﻬﻨﺪﺳﺔ‬‫اﻹﻋﺪادى‬ ‫اﻷول‬ ‫اﻟﺼﻒ‬ ‫أ‬/‫ﻣﺤﻤﻮد‬ ‫ﻣﺤﻤﺪ‬‫ت‬/٠١٢١١١٦٥٠١٢    )٥(‫ﺍﻟﺰﺍﻭﻳﺔ‬ ‫ﻗﻴﺎﺱ‬ ‫ﺃﻭﺟﺪ‬ ‫ﺍﻟﺘﺎﻟﻴﺔ‬ ‫ﺍﻷﺷﻜﺎﻝ‬ ‫ﻣﻦ‬ ‫ﻛﻞ‬ ‫ﰲ‬‫ﺷﻜﻞ‬ ‫ﻛﻞ‬ ‫ﺃﺳﻔﻞ‬ ‫ﺍﻟﻄﻠﻮﺑﺔ‬:           R)‫ب‬‫م‬O(=...........R)O‫م‬x(=...........R)h‫م‬‫ب‬(=...........                R)h‫م‬x(=...........R)h‫م‬x(=...........R)‫ب‬‫م‬x(=...........    )٦(‫ﺍﻟﺘﺎﻟﻴﺔ‬ ‫ﺍﻷﺷﻜﺎﻝ‬ ‫ﻣﻦ‬ ‫ﻛﻞ‬ ‫ﰲ‬: ‫م‬O)h‫م‬x(                R)x‫م‬O(=...........R)‫ب‬‫م‬i(=...........R)i‫م‬‫ب‬(=...........              O f ‫م‬ ١٥٠° ١٠٠° h h f O x i ‫م‬ ١١٠° ٤٥° ٩٠° ‫م‬ h f O x ٥٠° ١٠٠° ١٤٠° •• ‫م‬ ■ h f O x ٥٤° ٨٦°‫م‬ f h O • • x ١٢٠° • • ‫م‬ ١١٠° ٧٠° • h f O x ‫ﺯ‬‫ﺯ‬‫ﺯ‬ ‫ﺯ‬‫ﺯ‬‫ﺯ‬ ‫ﺯ‬ ‫م‬ x ١١٠° ٩٠° ‫ب‬ h O i ٥٠° ٤٥° h O ‫م‬‫ب‬ x ■ h ‫م‬ i f O x ‫ﺯ‬‫ﺯ‬ ‫ﺯ‬
  11. 11. ‫اﻟﺨﻮا‬‫ر‬‫اﻟ‬ ‫ﻓﻰ‬ ‫زﻣﻰ‬‫ﻬﻨﺪﺳﺔ‬‫اﻹﻋﺪادى‬ ‫اﻷول‬ ‫اﻟﺼﻒ‬ ‫أ‬/‫ﻣﺤﻤﻮد‬ ‫ﻣﺤﻤﺪ‬‫ت‬/٠١٢١١١٦٥٠١٢  ‫ﺍ‬ ‫ﺍﻟﺪﺭﺱ‬‫ﻟﺜﺎﻟﺚ‬     :h‫ب‬=Oxh‫ب‬≡Ox ‫ﺻﺤﻴﺢ‬ ‫ﻭﺍﻟﻌﻜﺲ‬    . :h‫ب‬≡Ox:h‫ب‬=Ox           :R)h‫ب‬O= (R)‫ع‬ ‫ص‬ ‫س‬( :)h‫ب‬O(≡)‫ع‬ ‫ص‬ ‫س‬( ‫ﺻﺤﻴﺢ‬ ‫ﻭﺍﻟﻌﻜﺲ‬        :)h‫ب‬O(≡)‫ع‬ ‫ص‬ ‫س‬( :R)h‫ب‬O= (R)‫ع‬ ‫ص‬ ‫س‬( َ ‫ﺃﻭﻻ‬:‫ﻣﺴﺘﻘﻴﻤﺘﲔ‬ ‫ﻗﻄﻌﺘﲔ‬ ‫ﺗﻄﺎﺑﻖ‬:-  f h Ox َ‫ﺛﺎﻧﻴﺎ‬:‫ﺯﺍﻭﻳﺘﲔ‬ ‫ﺗﻄﺎﺑﻖ‬:- ‫ﺯ‬ ‫ﺯ‬‫ﺯ‬ ‫ﺯ‬ ‫ﺯ‬‫ﺯ‬ ‫ﺯ‬ h‫ﺢ‬‫ﳒ‬ f O ‫ع‬ ‫ﺢ‬‫ﳒ‬ ‫س‬‫ص‬ ‫ﺯ‬   .
  12. 12. ‫اﻟﺨﻮا‬‫ر‬‫اﻟ‬ ‫ﻓﻰ‬ ‫زﻣﻰ‬‫ﻬﻨﺪﺳﺔ‬‫اﻹﻋﺪادى‬ ‫اﻷول‬ ‫اﻟﺼﻒ‬ ‫أ‬/‫ﻣﺤﻤﻮد‬ ‫ﻣﺤﻤﺪ‬‫ت‬/٠١٢١١١٦٥٠١٢  ‫ﻓﻤﺜﻼ‬:: )١(. ‫أن‬ ‫أي‬: h‫ب‬=‫ل‬ ‫س‬،‫ب‬O=‫ع‬ ‫ل‬ Ox=‫ص‬ ‫ع‬،hx=‫ص‬ ‫س‬ )٢(. ‫أن‬ ‫أي‬: R)h= (R)‫س‬(،R)‫ب‬= (R)‫ل‬( R)O= (R)‫ع‬(،R)x= (R)‫ص‬( h‫ب‬Ox≡‫ل‬ ‫س‬‫ص‬ ‫ع‬   َ‫ﺛﺎﻟﺜﺎ‬:‫ﻣﻀﻠﻌﲔ‬ ‫ﺗﻄﺎﺑﻖ‬)‫ﻫﻨﺪﺳﻴﲔ‬ ‫ﺷﻜﻠﲔ‬ ‫ﺃﻯ‬(:-    ‫ﺯ‬‫ﺯ‬‫ﺯ‬‫ﺯ‬ ‫ﺯ‬ ‫ﺯ‬‫ﺯ‬ ‫ﺯ‬   ‫ﲢﻘﻖ‬ ‫ﺇﺫﺍ‬ ‫ﺍﳌﻀﻠﻌﺎﻥ‬ ‫ﻳﺘﻄﺎﺑﻖ‬‫ﺍﻟﺸﺮﻃﺎﻥ‬  )١( )٢( ‫ﺻﺤﻴﺢ‬ ‫ﻭﺍﻟﻌﻜﺲ‬:‫ﻓﺈﻥ‬ ‫ﻣﻀﻠﻌﺎﻥ‬ ‫ﺗﻄﺎﺑﻖ‬ ‫ﺇﺫﺍ‬ ‫ﺃﻧﻪ‬ ‫ﺃﻱ‬  )١(  )٢(  O x‫ص‬ ‫ع‬ ‫ل‬ ‫س‬ h ‫ب‬
  13. 13. ‫اﻟﺨﻮا‬‫ر‬‫اﻟ‬ ‫ﻓﻰ‬ ‫زﻣﻰ‬‫ﻬﻨﺪﺳﺔ‬‫اﻹﻋﺪادى‬ ‫اﻷول‬ ‫اﻟﺼﻒ‬ ‫أ‬/‫ﻣﺤﻤﻮد‬ ‫ﻣﺤﻤﺪ‬‫ت‬/٠١٢١١١٦٥٠١٢  ‫ﻓﻤﺜﻼ‬::h‫ب‬Ox≡h‫ص‬ ‫س‬ ‫ب‬ ‫ﻓﺈ‬‫ن‬: )١(‫ب‬O=‫ب‬‫س‬ ،Ox=‫ص‬ ‫س‬ ،h x=h، ‫ص‬h‫ب‬ )٢(R)x= (R)‫ص‬( ،R)O= (R)‫س‬( ،R)xh‫ب‬= (R)‫ص‬h‫ب‬( ،R)h‫ب‬O= (R)h‫ب‬‫س‬( ‫ﺑﻨﻔﺴﻚ‬ ‫ﺣﺎﻭﻝ‬:‫ﺍﳌﻘﺎﺑﻞ‬ ‫ﺍﻟﺸﻜﻞ‬ ‫ﻓﻰ‬:-  ‫ص‬ ‫س‬&‫م‬≡h‫ب‬O‫م‬   ١(‫ص‬ ‫س‬≡.............٢(‫ص‬&................... = ٣(‫م‬O≡...............٤(h‫م‬............. =‫ﺳﻢ‬ ٥(h‫س‬............ =‫ﺳﻢ‬٦(R)‫ص‬= (R(......... ) ٧(R)O= (R(........ )٨(R)‫س‬= (R(......... ) ٩(R)O‫م‬h...... = (٥ ١٠(R)h.............. = (٥ ١١(R)&‫م‬O....... = (٥ ١٢(R)O‫س‬ ‫م‬....... = (٥ ‫ﺯ‬ ‫ﺯ‬ ‫ﺯ‬ ‫ﺯ‬ ‫ﺯ‬ ‫ﺯ‬ ‫ﺯ‬‫ﺯ‬ x h ‫ص‬ ‫س‬ ‫ب‬ O ‫ﺯ‬ ‫ﺯ‬ ‫ﺯ‬ ‫ﺯ‬ ‫ﺯ‬ ‫ﺯ‬‫ﺯ‬ ‫ﺯ‬ ‫ﺯ‬ ‫ﺯ‬ ‫ص‬ &O ‫ب‬ ‫س‬h ‫م‬ ٦٥٥ ٦‫ﺳﻢ‬ ■ ■
  14. 14. ‫اﻟﺨﻮا‬‫ر‬‫اﻟ‬ ‫ﻓﻰ‬ ‫زﻣﻰ‬‫ﻬﻨﺪﺳﺔ‬‫اﻹﻋﺪادى‬ ‫اﻷول‬ ‫اﻟﺼﻒ‬ ‫أ‬/‫ﻣﺤﻤﻮد‬ ‫ﻣﺤﻤﺪ‬‫ت‬/٠١٢١١١٦٥٠١٢   )(‫ﻳﺄﺗﻲ‬ ‫ﻣﺎ‬ ‫ﺃﻛﻤﻞ‬:- ١(‫ﻛﺎﻧﺘﺎ‬ ‫اذا‬ ‫اﻟﻤﺴﺘﻘﯿﻤﺘﺎن‬ ‫اﻟﻘﻄﻌﺘﺎن‬ ‫ﺗﺘﻄﺎﺑﻖ‬............................. ٢(‫ﻛﺎﻧﺘﺎ‬ ‫اذا‬ ‫اﻟﺰاوﯾﺘﺎن‬ ‫ﺗﺘﻄﺎﺑﻖ‬............................................ ٣(‫اذ‬ ‫اﻟﻤﻀﻠﻌﺎن‬ ‫ﯾﺘﻄﺎﺑﻖ‬‫ﻛﻞ‬ ‫ﯾﻄﺎﺑﻖ‬ ‫ﺑﺤﯿﺚ‬ ‫رءوﺳﯿﮭﻤﺎ‬ ‫ﺑﯿﻦ‬ ‫ﺗﻘﺎﺑﻞ‬ ‫وﺟﺪ‬.........‫وﻛﻞ‬...........‫اﻟﻤﻀﻠﻊ‬ ‫ﻓﻰ‬ ‫ﻓﻰ‬ ‫ﻧﻈﯿﺮه‬ ‫اﻻول‬.............................. ٥(‫ﺷﻜﻠﯿﻦ‬ ‫اﻟﻰ‬ ‫ﯾﻘﺴﻤﮫ‬ ‫اﻟﺸﻜﻞ‬ ‫ﺗﻤﺎﺛﻞ‬ ‫ﻣﺤﻮر‬............................. ٦(‫ﻛﺎن‬ ‫إذا‬h‫ب‬≡Ox‫ﻓﺎن‬h‫ب‬=........................ ٧(‫ﻛﺎن‬ ‫إذا‬)h(≡)‫ب‬(‫وﻛﺎن‬R)h= (٥٠٥ ‫ﻓﺈ‬‫ن‬R)‫ب‬........ = (٥ ٨(‫ص‬ ‫س‬ ‫ﻛﺎن‬ ‫اذا‬≡h‫ب‬‫ﻓﺈ‬‫ن‬:‫ص‬ ‫س‬–h‫ب‬................... = ٩(‫اﻟﻤﻀﻠﻊ‬ ‫ﻛﺎن‬ ‫إذا‬h‫ب‬Ox≡‫ل‬ ‫ع‬ ‫ص‬ ‫س‬ ‫اﻟﻤﻀﻠﻊ‬‫ﻓﺈ‬‫ن‬:R)hOx................. = ( ١٠(‫ﻛﺎﻧﺖ‬ ‫اذا‬O‫ﻣﻨﺘﺼﻒ‬h‫ب‬‫ﻓﺈ‬‫ن‬hO..........‫ب‬O )(‫ﺍﳌﻘﺎﺑﻞ‬ ‫ﺍﻟﺸﻜﻞ‬ ‫ﰲ‬:-:- ١(‫اﻟﺮأس‬‫ب‬‫ﺗﻨﺎﻇﺮ‬‫ا‬‫ﻟﺮأس‬............ ٢(‫اﻟﻤﻀﻠﻊ‬h‫ب‬O x≡‫اﻟﻤﻀﻠﻊ‬....... ٣(h‫ب‬≡.................... ٤(‫ل‬&............. =‫ﺳﻢ‬ ٥(R)h= (R(....... ) ٦(‫ص‬ ‫س‬.............. = ٧(R)‫ص‬..................... = ( ٨(Ox.......................... = ٩(xi‫ـــ‬‫ص‬ ‫ع‬=.................. )(‫ﺍﳌﻘﺎﺑﻞ‬ ‫ﺍﻟﺸﻜﻞ‬ ‫ﰲ‬:-h‫ب‬O‫و‬≡‫اﻟﻤﻀﻠﻊ‬ixO‫و‬:- ١(h‫ب‬.......................... = ٢(h‫و‬.......................... = ٣(Ox...................... = ٤(O‫ﺿﻠﻊ‬ ‫و‬................. ٥(R)i= (R(........ ) ٦(R)‫ب‬= (R(........... ) ٧(R)‫و‬Ox= (R(.......... )٨(R)i‫و‬O...... = (٥ ٩(‫ب‬x........ =‫ﺳﻢ‬١٠(R)‫و‬Ox...... = (٥ ١١(R)h‫و‬i............................ = (٥ ١٢(‫اﻟﻤﻘﺎﺑﻞ‬ ‫اﻟﺸﻜﻞ‬ ‫ﺗﻤﺎﺛﻞ‬ ‫ﻣﺤﻮر‬................. ‫ﺢ‬‫ﳒ‬ × ‫ﺽ‬‫ﻆ‬‫ﻇ‬ ‫ل‬ ‫س‬‫ص‬ ‫ع‬ ‫ﺢ‬‫ﳒ‬ × ‫ﺽ‬‫ﻆ‬‫ﻇ‬ ‫أ‬ ‫ب‬‫ﺟـ‬ ‫ء‬ ‫ﺯ‬‫ﺯ‬ ‫ﺯ‬ ‫ﺯ‬ ‫ﺯ‬ ‫ﺯ‬ ‫ﺯ‬ ‫ﺯ‬ ‫ﺯ‬ ‫ﺯ‬ ‫ﺯ‬ ‫ﺯ‬ ‫ﺯ‬  h ١٢٠٥ ٥‫ﺳﻢ‬ ‫و‬ i x O ‫ب‬
  15. 15. ‫اﻟﺨﻮا‬‫ر‬‫اﻟ‬ ‫ﻓﻰ‬ ‫زﻣﻰ‬‫ﻬﻨﺪﺳﺔ‬‫اﻹﻋﺪادى‬ ‫اﻷول‬ ‫اﻟﺼﻒ‬ ‫أ‬/‫ﻣﺤﻤﻮد‬ ‫ﻣﺤﻤﺪ‬‫ت‬/٠١٢١١١٦٥٠١٢  ‫ﺍ‬ ‫ﺍﻟﺪﺭﺱ‬‫ﻟﺮﺍﺑﻊ‬     :h‫ب‬،‫ب‬O،hO :)h(،)‫ب‬(،)O(           h‫ب‬O‫ع‬ ‫ص‬ ‫س‬ ،: )١(h‫ب‬=‫ص‬ ‫س‬،hO=، ‫ع‬ ‫س‬‫ب‬O=‫ع‬ ‫ص‬ )٢(R)h= (R)‫س‬(،R)‫ب‬= (R)‫ص‬(،R)O= (R)‫ع‬( :∆h‫ب‬O≡´‫ع‬ ‫ص‬ ‫س‬ ‫ﺍﳌﻘﺎﺑﻞ‬ ‫ﺍﻟﺸﻜﻞ‬ ‫ﰲ‬:-‫إ‬‫ﺛﺒﺖ‬‫أ‬‫ن‬:h∆‫ب‬O≡∆xi‫و‬ h∆∆‫ب‬O،xi‫و‬ h‫ب‬=xi ‫ﻓﯿﮭﻤﺎ‬R)‫ب‬(=R)i( ‫ب‬‫ﺟـ‬=i‫و‬ Eh∆‫ب‬O≡∆xi‫و‬ hO=x‫و‬ R)h= (R)x( R)O= (R)‫و‬(  ‫ﺯ‬‫ﺯ‬‫ﺯ‬ ‫ﺯ‬‫ﺯ‬‫ﺯ‬ ‫ﺯ‬‫ﺯ‬ ‫ﺯ‬                ‫ﺯ‬ ‫ﺯ‬ ‫ﺯ‬ ‫ﺯ‬‫ﺯ‬ ‫ﺯ‬ h fO h f‫ع‬ ‫ص‬ O ‫س‬ * * h ‫ب‬O x i‫و‬
  16. 16. ‫اﻟﺨﻮا‬‫ر‬‫اﻟ‬ ‫ﻓﻰ‬ ‫زﻣﻰ‬‫ﻬﻨﺪﺳﺔ‬‫اﻹﻋﺪادى‬ ‫اﻷول‬ ‫اﻟﺼﻒ‬ ‫أ‬/‫ﻣﺤﻤﻮد‬ ‫ﻣﺤﻤﺪ‬‫ت‬/٠١٢١١١٦٥٠١٢  ‫ﺍﳌﻘﺎﺑﻞ‬ ‫ﺍﻟﺸﻜﻞ‬ ‫ﰲ‬:-‫أ‬‫ﺛﺒﺖ‬‫أ‬‫ن‬:∆h‫ب‬O≡∆xi‫و‬ h∆∆‫ب‬O،xi‫و‬ R)O= (R)‫و‬( ‫ﻓﯿﮭﻤﺎ‬R)‫ب‬= (R)i( ‫ب‬‫ﺟـ‬=i‫و‬ Eh∆‫ب‬O≡∆xi‫و‬ h‫ب‬=xi hO=x‫و‬ R)h= (R)x( ‫ﺍﳌﻘﺎﺑﻞ‬ ‫ﺍﻟﺸﻜﻞ‬ ‫ﰲ‬:-‫أ‬‫ﺛﺒﺖ‬‫أ‬‫ن‬:h∆‫ب‬O≡∆xi‫و‬ ∆∆h‫ب‬O،xi‫و‬ h‫ب‬=xi ‫ﻓﯿﮭﻤﺎ‬hO=x‫و‬ ‫ب‬O=i‫و‬ E∆h‫ب‬O≡∆xi‫و‬‫ان‬ ‫وﻳﻨﺘﺞ‬: R)‫ب‬= (R)i( R)O= (R)‫و‬( R)h= (R)x(     ‫ﺯ‬ ‫ﺯ‬ ‫ﺯ‬ ‫ﺯ‬‫ﺯ‬ ‫ﺯ‬    i •• * h fO * x ‫و‬ ‫ﺯ‬‫ﺯ‬ ‫ﺯ‬ ‫ﺯ‬ ‫ﺯ‬‫ﺯ‬ i h fO x ‫و‬  
  17. 17. ‫اﻟﺨﻮا‬‫ر‬‫اﻟ‬ ‫ﻓﻰ‬ ‫زﻣﻰ‬‫ﻬﻨﺪﺳﺔ‬‫اﻹﻋﺪادى‬ ‫اﻷول‬ ‫اﻟﺼﻒ‬ ‫أ‬/‫ﻣﺤﻤﻮد‬ ‫ﻣﺤﻤﺪ‬‫ت‬/٠١٢١١١٦٥٠١٢  ‫ﺍﳌﻘﺎﺑﻞ‬ ‫ﺍﻟﺸﻜﻞ‬ ‫ﰲ‬:-‫أ‬‫ﺛﺒﺖ‬‫أ‬‫ن‬:h∆‫ب‬O≡∆xi‫و‬ ∆∆h‫ب‬O،xi‫و‬ ‫ب‬O=i‫و‬ ‫ﻓﯿﮭﻤﺎ‬hO=x‫و‬ R)‫ب‬(=R)i= (٩٠٥ E∆h‫ب‬O≡∆xi‫و‬‫ان‬ ‫وﻳﻨﺘﺞ‬: h‫ب‬=xi R)O(=R)‫و‬( R)h= (R)x( ‫ﺍﳌﻘﺎﺑﻞ‬ ‫ﺍﻟﺸﻜﻞ‬ ‫ﰲ‬:-     ∆∆h‫ب‬x،hOx h‫ب‬=hO ‫ﻓﯿﮭﻤﺎ‬‫ب‬x=Ox hx‫ﻣﺸﺘﺮك‬ ‫ﺿﻠﻊ‬ E∆h‫ب‬x≡h∆Ox‫وﻳﻨﺘﺞ‬‫ان‬ R)‫ب‬(=R)O( R)‫ب‬hx(=R)Ohx( R)‫ب‬xh(=R)Oxh( ‫اﻟﺘﻄﺎﺑﻖ‬ ‫ﺣﺎﻟﺔ‬:      ‫ﺯ‬ ‫ﺯ‬ ‫ﺯ‬‫ﺯ‬ ‫ﺯ‬ ‫ﺯ‬ hx fOi‫و‬ ■■ ‫ﺯ‬‫ﺯ‬ ‫ﺯ‬‫ﺯ‬ ‫ﺯ‬‫ﺯ‬  f x O h
  18. 18. ‫اﻟﺨﻮا‬‫ر‬‫اﻟ‬ ‫ﻓﻰ‬ ‫زﻣﻰ‬‫ﻬﻨﺪﺳﺔ‬‫اﻹﻋﺪادى‬ ‫اﻷول‬ ‫اﻟﺼﻒ‬ ‫أ‬/‫ﻣﺤﻤﻮد‬ ‫ﻣﺤﻤﺪ‬‫ت‬/٠١٢١١١٦٥٠١٢  ‫ﺍﳌﻘﺎﺑﻞ‬ ‫ﺍﻟﺸﻜﻞ‬ ‫ﰲ‬:-R)O(‫؟‬  ∆∆h‫م‬O،‫ب‬‫م‬x ‫م‬h=‫م‬‫ب‬ R)h= (R)‫ب‬( R)h‫م‬O= (R)‫ب‬‫م‬x= (٨٠٥ . E∆h‫م‬O≡∆‫ب‬‫م‬x‫وﻳﻨﺘﺞ‬‫أ‬‫ن‬R)O= (R)x= (٦٠٥ ‫ﺍﳌﻘﺎﺑﻞ‬ ‫ﺍﻟﺸﻜﻞ‬ ‫ﰲ‬:-‫ﻣﺎﻳﺄﺗﻰ‬ ‫أﻛﻤﻞ‬:- ∆∆............،............. ١.......................... ( ‫ﻓﯿﮭﻤﺎ‬٢........................ ( ٣........................ ( E∆............≡∆.............‫وﻳﻨﺘﺞ‬‫ا‬‫ن‬:- ١........................... ( ٢........................... ( ٣.......................... ( ‫اﻟﺘﻄﺎﺑﻖ‬ ‫ﺣﺎﻟﺔ‬.............................................................. : ‫ﺍﳌﻘﺎﺑﻞ‬ ‫ﺍﻟﺸﻜﻞ‬ ‫ﰲ‬:-‫ﻣﺎﻳﺄﺗﻰ‬ ‫أﻛﻤﻞ‬:- ١(‫ل‬ ‫س‬................. = ٢(R)‫س‬....... = (٥ ٣(‫ﺿﻠﻊ‬ ‫ل‬ ‫ص‬.............. ٤(‫ع‬ ‫ص‬................. = ٥(R)‫ع‬ ‫ص‬ ‫س‬= (R....... = (............)٥ ٦(R)‫ص‬ ‫ل‬ ‫س‬= (R...... )........... = (....٥ ‫ﺍﳌﻘﺎﺑﻞ‬ ‫ﺍﻟﺸﻜﻞ‬ ‫ﰲ‬:- R)hfO(‫؟‬ ‫ﺯ‬ ‫ﺯ‬‫ﺯ‬ ‫ﺯ‬ ‫ﺯ‬‫ﺯ‬ ‫ﺯ‬ ‫ﺯ‬ ‫ﺯ‬ ‫ﺯ‬ h fxO • • ٨٠٥ ٦٠٥ ‫ص‬ ‫ع‬ ‫ل‬ ‫س‬ ٥٠٥ ‫ﺯ‬f O x h ٥٠٥ ١١٠٥ h ‫ب‬ ٥ O x ‫م‬
  19. 19. ‫اﻟﺨﻮا‬‫ر‬‫اﻟ‬ ‫ﻓﻰ‬ ‫زﻣﻰ‬‫ﻬﻨﺪﺳﺔ‬‫اﻹﻋﺪادى‬ ‫اﻷول‬ ‫اﻟﺼﻒ‬ ‫أ‬/‫ﻣﺤﻤﻮد‬ ‫ﻣﺤﻤﺪ‬‫ت‬/٠١٢١١١٦٥٠١٢  ‫ﺍ‬ ‫ﺍﻟﺪﺭﺱ‬‫ﳋﺎﻣﺲ‬   )٣،٥(،)٤،٦( )١،٥(،)٢،٦(،)٤،٧(،)٣،٨( )٤،٥(،)٣،٦( //،:- R)٣= (R)٥( R)٤= (R)٦( R)١= (R)٥( R)٢= (R)٦( R)٤= (R)٨( R)٣= (R)٧( R)٤+ (R)٥= (١٨٠٥  R)٣+ (R)٦= (١٨٠٥   ‫ﳌﺴﺘﻘﻴﻤﲔ‬ ‫ﻣﺴﺘﻘﻴﻢ‬ ‫ﻗﻄﻊ‬ ‫ﻣﻦ‬ ‫ﺍﻟﻨﺎﲡﺔ‬ ‫ﺍﻟﺰﻭﺍﻳﺎ‬:- )(:- )(:- )(:- ٦ ١  ٢ ٤ ٥ ٧٨  ٣ ‫ﻣﺘﻮﺍﺯﻳﲔ‬ ‫ﳌﺴﺘﻘﻴﻤﲔ‬ ‫ﻣﺴﺘﻘﻴﻢ‬ ‫ﻗﻄﻊ‬ ‫ﻣﻦ‬ ‫ﺍﻟﻨﺎﲡﺔ‬ ‫ﺍﻟﺰﻭﺍﻳﺎ‬ ‫ﺃﺯﻭﺍﺝ‬ ‫ﺑﲔ‬ ‫ﺍﻟﻌﻼﻗﺔ‬:- ‫ﻓ‬ ‫ﻣﺘﻮﺍﺯﻳﻴﻦ‬ ‫ﻣﺴﺘﻘﻴﻤﻴﻦ‬ ‫ﻣﺴﺘﻘﻴﻢ‬ ‫ﻗﻄﻊ‬ ‫ﺍﺫﺍ‬‫ﺈ‬‫ﻥ‬:-       ١٢ ٣ ٤ ٥٦ ٧ ٨   
  20. 20. ‫اﻟﺨﻮا‬‫ر‬‫اﻟ‬ ‫ﻓﻰ‬ ‫زﻣﻰ‬‫ﻬﻨﺪﺳﺔ‬‫اﻹﻋﺪادى‬ ‫اﻷول‬ ‫اﻟﺼﻒ‬ ‫أ‬/‫ﻣﺤﻤﻮد‬ ‫ﻣﺤﻤﺪ‬‫ت‬/٠١٢١١١٦٥٠١٢  ‫ﺑﺎﻟﻌﻼﻣﺔ‬ ‫ﺇﻟﻴﻬﺎ‬ ‫ﺍﳌﺸﺎﺭ‬ ‫ﺍﻟﺰﺍﻭﻳﺔ‬ ‫ﻗﻴﺎﺱ‬ ‫ﺃﻭﺟﺪ‬ ‫ﺍﻵﺗﻴﺔ‬ ‫ﺍﻷﺷﻜﺎﻝ‬ ‫ﻣﻦ‬ ‫ﻛﻞ‬ ‫ﻓﻰ‬)‫؟‬(‫ﺍﻟﺴﺒﺐ‬ ‫ﺫﻛﺮ‬ ‫ﻣﻊ‬:-  ‫ﺷﻜﻞ‬)١(:R)‫ن‬ ‫م‬x(=°R)‫ن‬ ‫م‬x(=R)h‫ن‬ ‫م‬()( ‫ﺷﻜﻞ‬)٢(:R)‫ن‬ ‫و‬ ‫ع‬(=°R)‫و‬ ‫ع‬i(=R)‫س‬i‫م‬(=°)( :R)‫ن‬ ‫و‬ ‫ع‬(=°-°=° ‫ﺷﻜﻞ‬)٣(:R)fOx(=°:R)f(=R)h(=°)(  )f()O(  R)fOx(=°‫ـــ‬°=°    ‫ﺍﳌﻘﺎﺑﻞ‬ ‫ﺍﻟﺸﻜﻞ‬ ‫ﰲ‬:- ‫اوﺟﺪ‬:R)f(،R)O(،R)fhO(‫؟‬        xi........... //،hf R)f= (R........... = (......... )٥ ‫ﺑـ‬..............)١( xi........... //،hO R)O= (R........... = (.............. )٥ ‫ﺑـ‬.........)٢( R)xhi................ = (٥  R)fhO= (١٨٠٥ –......... )٥ ............ +٥ ( R)hfO= (١٨٠٥ –............٥ ........... =٥ )٣(   ‫م‬ x ‫؟‬ i h f O ° hf Ox i ‫ن‬ ‫و‬ ° ‫؟‬› › i ‫س‬‫ص‬ ‫و‬ ‫م‬ ‫ل‬ ‫ع‬ ‫ن‬ ‫؟‬ ° › › ‫ﺷﻜﻞ‬)٢( ‫ﺷﻜﻞ‬)١(‫ﺷﻜﻞ‬)٣( ‫ﺯ‬‫ﺯ‬‫ﺯ‬ ‫ﺯ‬‫ﺯ‬‫ﺯ‬ ‫ﺯ‬ ‫ﺯ‬‫ﺯ‬‫ﺯ‬ ‫ﺯ‬‫ﺯ‬ ‫ﺯ‬ › › ‫ﺯ‬ ‫ﺯ‬‫ﺯ‬ ‫ﺯ‬ ‫ﺯ‬ ‫ﺯ‬ ‫ﺯ‬ ‫ﺯ‬ h O x ٧٠٥ f ٥٠٥ i 
  21. 21. ‫اﻟﺨﻮا‬‫ر‬‫اﻟ‬ ‫ﻓﻰ‬ ‫زﻣﻰ‬‫ﻬﻨﺪﺳﺔ‬‫اﻹﻋﺪادى‬ ‫اﻷول‬ ‫اﻟﺼﻒ‬ ‫أ‬/‫ﻣﺤﻤﻮد‬ ‫ﻣﺤﻤﺪ‬‫ت‬/٠١٢١١١٦٥٠١٢  ‫ﺍﳌﻘﺎﺑﻞ‬ ‫ﺍﻟﺸﻜﻞ‬ ‫ﰲ‬:-R)hOi(‫؟‬     hf//Ox،............ R)hOx= (١٨٠٥ –........... .............. = Ox//‫و‬i،........... R)xOi.............. = (–..................=................ R)hOi(.................... =+.....................=...............٥ R)hOi= (٣٦٠٥ –..........=...............٥ ‫ﺍﳌﻘﺎﺑﻞ‬ ‫ﺍﻟﺸﻜﻞ‬ ‫ﰲ‬:-R)xOi(‫؟‬  hf//Ox،fO R)xOf= (١٨٠٥ –٦٠٥ =١٢٠٥  =٣٦٠٥   R)xOi(=٣٦٠٥ –)١٢٠٥ +١٢٠٥ ( =٣٦٠٥ –٢٤٠٥ =١٢٠٥ ‫ﺍﳌﻘﺎﺑﻞ‬ ‫ﺍﻟﺸﻜﻞ‬ ‫ﰲ‬:-R)ihf(،R)O(،R)ihO(‫؟‬  hi//fO،hf R)ihf(=R)f= (٥٠٥ )١( hi//fO،Oh R)O(=R)xhi= (٧٠٥ )٢( R)xhO= (١٨٠٥ )( R)fhO= (١٨٠٥ –)٧٠٥ +٥٠٥ ( =١٨٠٥ –٥ ١٢٠=٦٠٥ R)ihO= (٥٠٥ +٦٠٥ =١١٠٥ )٣( ‫ﺯ‬ ‫ﺯ‬ ‫ﺯ‬ ‫ﺯ‬ ‫ﺯ‬ O ‫و‬i h f x ٤٠٥ ٣٠٥ f ‫ﺯ‬ ‫ﺯ‬ ‫ﺯ‬ ‫ﺯ‬ ‫ﺯ‬ ‫ﺯ‬‫ﺯ‬ ‫ﺯ‬ ‫ﺯ‬ ‫ﺯ‬ ‫ﺯ‬h ٥٠٥ i fO x ٧٠٥ ١٢٠ ٥ O hx i ٦٠ ٥ ‫ﺯ‬ ‫ﺯ‬
  22. 22. ‫اﻟﺨﻮا‬‫ر‬‫اﻟ‬ ‫ﻓﻰ‬ ‫زﻣﻰ‬‫ﻬﻨﺪﺳﺔ‬‫اﻹﻋﺪادى‬ ‫اﻷول‬ ‫اﻟﺼﻒ‬ ‫أ‬/‫ﻣﺤﻤﻮد‬ ‫ﻣﺤﻤﺪ‬‫ت‬/٠١٢١١١٦٥٠١٢  ‫ﻳﻜﻮﻥ‬ ‫ﳌﺎﺫﺍ‬ ‫ﺑﲔ‬ ‫ﺍﻵﺗﻴﺔ‬ ‫ﺍﻷﺷﻜﺎﻝ‬ ‫ﻣﻦ‬ ‫ﻛﻞ‬ ‫ﻓﻰ‬hf//Ox‫ﺍﻟﺴﺒﺐ‬ ‫ﺫﻛﺮ‬ ‫ﻣﻊ‬:- fh//Ox‫ﻷﻥ‬:fh//Ox‫ﻷﻥ‬:fh//Ox‫ﻷﻥ‬: R)ihO= (R)ihO= (°R)ihO= (R)ihO= (°R)ihO= (R)ihO= (° )) () ( (   ‫ﻣﺴﺘﻘﻴﻤﲔ‬ ‫ﺗﻮﺍﺯﻱ‬ ‫ﺷﺮﻁ‬:- ‫ﺍﻵﺗﻴﺔ‬ ‫ﺍﻟﺤﺎﻻﺕ‬ ‫ﺇﺣﺪﻯ‬ ‫ﻭﺣﺪﺛﺖ‬ ‫ﺛﺎﻟﺚ‬ ‫ﻣﺴﺘﻘﻴﻢ‬ ‫ﻗﻄﻌﻬﻤﺎ‬ ‫ﺇﺫﺍ‬ ‫ﺍﻟﻤﺴﺘﻘﻴﻤﺎﻥ‬ ‫ﻳﺘﻮﺍﺯﻯ‬:- )١( )٢( )٣( ° ‫م‬ › › hf Ox i ‫و‬ ° ‫ن‬› › i hf ‫و‬ ‫م‬ x O ‫ن‬ ‫؟‬ ° ° ‫م‬ O x h f i‫و‬ ‫ن‬ °° ‫ﻫﻨﺪﺳﻴﺔ‬ ‫ﺣﻘﺎﺋﻖ‬:- )( . )(  )(   ‫ﺯ‬‫ﺯ‬‫ﺯ‬‫ﺯ‬‫ﺯ‬‫ﺯ‬
  23. 23. ‫اﻟﺨﻮا‬‫ر‬‫اﻟ‬ ‫ﻓﻰ‬ ‫زﻣﻰ‬‫ﻬﻨﺪﺳﺔ‬‫اﻹﻋﺪادى‬ ‫اﻷول‬ ‫اﻟﺼﻒ‬ ‫أ‬/‫ﻣﺤﻤﻮد‬ ‫ﻣﺤﻤﺪ‬‫ت‬/٠١٢١١١٦٥٠١٢  ‫ﺍﳌﻘﺎﺑﻞ‬ ‫ﺍﻟﺸﻜﻞ‬ ‫ﰲ‬:-x‫؟‬ ‫ص‬     :hx//‫س‬‫ص‬//fO،hf ،h‫س‬=‫س‬f :x‫ص‬=‫ص‬O=٢‫ﺳﻢ‬ ‫ﺍﳌﻘﺎﺑﻞ‬ ‫ﺍﻟﺸﻜﻞ‬ ‫ﰲ‬:-h‫؟‬ ‫ص‬     :fO//x‫و‬//‫س‬i//‫ص‬‫ع‬،h‫ع‬ ،h‫و‬=‫و‬i=i‫ع‬ :hx=x‫س‬=‫س‬‫ص‬=٥‫ﺳﻢ‬ :h‫ص‬=١٥‫ﺳﻢ‬ ‫ﺍﳌﻘﺎﺑﻞ‬ ‫ﺍﻟﺸﻜﻞ‬ ‫ﰲ‬:-‫ص‬O‫؟‬  ‫أن‬ ‫ﺣﯿﺚ‬:hx//‫س‬‫ص‬//‫ع‬‫ل‬//fO،h‫ب‬،xO ،h‫س‬=‫س‬‫ع‬=‫ع‬f x‫ص‬=‫ص‬‫ل‬=‫ل‬O==٤‫ﺳﻢ‬ :‫ص‬O=٤+٤=٨‫ﺳﻢ‬ h ‫ص‬ x O f ‫س‬ ٢‫ﺳﻢ‬ ١٢ ٣ ١٢‫ﺳﻢ‬ h ‫ب‬ ‫س‬ ‫ع‬ x ‫ص‬ ‫ل‬ O x h fO ‫س‬ ‫ص‬‫ع‬ i ‫و‬ ٥‫ﺳﻢ‬

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