2 cours math tcs

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‫اﻟﺤﺴﺎب اﻟﻤﺘﺠﻬﻲ‬

‫‪ -(I‬ﺗﺴﺎوي ﻣﺘﺠﻬﺘﻴﻦ – ﺟﻤﻊ اﻟﻤﺘﺠﻬﺎت‬ ‫‪ -1‬أﻧﺸﻄﺔ‬ ‫‪ -1‬ﻟﻴﻜﻦ ‪ A‬و ‪ B‬و ‪ C‬و ‪ D‬أرﺑﻊ ﻧﻘﻂ ﻣﻦ اﻟﻤﺴﺘﻮى‬

‫أﻧﺸﺊ ‪ M‬و ‪ N‬ﺣﻴﺚ ‪ BM = AC‬و ‪AN = AC + AD‬‬ ‫‪ -2‬ﻟﻴﻜﻦ ‪ ABCD‬ﻣﺘﻮازي اﻷﺿﻼع ﻣﺮآﺰﻩ ‪O‬‬ ‫أﻧﺸﺊ ‪ M‬ﺣﻴﺚ ‪ OM = AB + AD‬و أﻧﺸﺊ ‪ I‬ﺣﻴﺚ ‪DI = OD − BC‬‬ ‫أﺛﺒﺖ أن ‪CM = AO‬‬ ‫اﺧﺘﺼﺮ ‪BE + DF + EF + AB + ED + FA‬‬ ‫‪ -3‬ﻟﻴﻜﻦ ‪ A‬و ‪ B‬و ‪ C‬و ‪ D‬و ‪ E‬ﻧﻘﻄﺎ‬ ‫ﻗﺎرن ‪ MN‬و ‪BD‬‬

‫‪ -2‬ﺗﺴﺎوي ﻣﺘﺠﻬﺘﻴﻦ‬ ‫ب‪ -‬ﺗﻌﺮﻳﻒ‬ ‫ﺗﻜﻮن ﻣﺘﺠﻬﺘﺎن ﻣﺘﺴﺎوﻳﺘﺎن اذا آﺎن ﻟﻬﻤﺎ ﻧﻔﺲ اﻻﺗﺠﺎﻩ و ﻧﻔﺲ اﻟﻤﻨﺤﻰ و ﻧﻔﺲ اﻟﻤﻨﻈﻢ‬

‫‪u‬‬

‫‪om‬‬ ‫‪i.c‬‬

‫ﻧﻜﺘﺐ ‪u = AB = CD = EF‬‬

‫‪ad‬‬

‫ج‪ -‬اﻟﻤﺘﺠﻬﺔ اﻟﻤﻨﻌﺪﻣﺔ‬

‫‪ow‬‬ ‫‪.m‬‬ ‫‪w‬‬

‫*‪ -‬اﻟﻤﺘﺠﻬﺔ اﻟﻤﻨﻌﺪﻣﺔ ‪: 0‬‬ ‫د – ﺧﺎﺻﻴﺎت‬ ‫ﺧﺎﺻﻴﺔ‪1‬‬ ‫‪ A‬و ‪ B‬و ‪ C‬و ‪ D‬أرﺑﻊ ﻧﻘﻂ ﻣﻦ اﻟﻤﺴﺘﻮى‬

‫‪ah‬‬

‫‪ 0 = MM‬ﻟﻜﻞ ﻧﻘﻄﺔ ﻧﻘﻄﺔ ‪ M‬ﻣﻦ اﻟﻤﺴﺘﻮى‬

‫‪w‬‬

‫‪w‬‬

‫‪ AB = CD‬إذا وﻓﻘﻂ إذا آﺎن ﻟﻠﻘﻄﻌﺘﻴﻦ ] ‪ [ AD‬و ] ‪ [ BC‬ﻧﻔﺲ اﻟﻤﻨﺘﺼﻒ‬

‫‪I‬‬

‫ﻣﻨﺘﺼﻒ اﻟﻘﻄﻌﺘﻴﻦ ] ‪ [ AD‬و ] ‪[ BC‬‬

‫ﺧﺎﺻﻴﺔ‪2‬‬ ‫إذا آﺎﻧﺖ ‪ A‬و ‪ B‬و ‪ C‬و ‪ D‬أرﺑﻊ ﻧﻘﻂ ﻏﻴﺮ ﻣﺴﺘﻘﻴﻤﻴﺔ ﻓﻲ اﻟﻤﺴﺘﻮى ﻓﺎن ‪:‬‬ ‫‪ AB = CD‬إذا وﻓﻘﻂ إذا آﺎن ‪ ABDC‬ﻣﺘﻮازي اﻷﺿﻼع‬ ‫ﻧﺘﻴﺠﺔ‬ ‫ﻟﺘﻜﻦ ‪ A‬و ‪ B‬و ‪ C‬و ‪ D‬أرﺑﻊ ﻧﻘﻂ ﻣﻦ اﻟﻤﺴﺘﻮى‬

‫‪ AB = CD‬إذا وﻓﻘﻂ إذا آﺎن ‪AC = BD‬‬ ‫‪ AB = CD‬إذا وﻓﻘﻂ إذا آﺎن ‪DB = CA‬‬

‫)ﺗﺒﺪﻳﻞ اﻟﻮﺳﻄﻴﻦ(‬ ‫)ﺗﺒﺪﻳﻞ اﻟﻄﺮﻓﻴﻦ(‬

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