Tạ Hà Gia Bảo
Giới thiệu về bản thân
Thử phiên bản mới
Chào mừng bạn đến với trang cá nhân của Tạ Hà Gia Bảo
0
0
0
0
0
0
0
2025-12-15 19:22:57
a) Chứng minh AMMD=BNNCthe fraction with numerator cap A cap M and denominator cap M cap D end-fraction equals the fraction with numerator cap B cap N and denominator cap N cap C end-fraction𝐴𝑀𝑀𝐷=𝐵𝑁𝑁𝐶
- Xét tam giác ADCcap A cap D cap C𝐴𝐷𝐶có MPcap M cap P𝑀𝑃song song với CDcap C cap D𝐶𝐷.
- Theo định lý Thales, tỉ số AMMDthe fraction with numerator cap A cap M and denominator cap M cap D end-fraction𝐴𝑀𝑀𝐷bằng APPCthe fraction with numerator cap A cap P and denominator cap P cap C end-fraction𝐴𝑃𝑃𝐶.
- Xét tam giác ABCcap A cap B cap C𝐴𝐵𝐶có PNcap P cap N𝑃𝑁song song với ABcap A cap B𝐴𝐵.
- Theo định lý Thales, tỉ số BNNCthe fraction with numerator cap B cap N and denominator cap N cap C end-fraction𝐵𝑁𝑁𝐶bằng APPCthe fraction with numerator cap A cap P and denominator cap P cap C end-fraction𝐴𝑃𝑃𝐶.
- Từ hai điều trên, suy ra AMMD=BNNCthe fraction with numerator cap A cap M and denominator cap M cap D end-fraction equals the fraction with numerator cap B cap N and denominator cap N cap C end-fraction𝐴𝑀𝑀𝐷=𝐵𝑁𝑁𝐶.
- Từ giả thiết MD=2MAcap M cap D equals 2 cap M cap A𝑀𝐷=2𝑀𝐴, suy ra AMMD=12the fraction with numerator cap A cap M and denominator cap M cap D end-fraction equals 1 over 2 end-fraction𝐴𝑀𝑀𝐷=12.
- Áp dụng định lý Thales cho tam giác ADCcap A cap D cap C𝐴𝐷𝐶với MP//CDcap M cap P / / cap C cap D𝑀𝑃//𝐶𝐷, ta có MPCD=AMADthe fraction with numerator cap M cap P and denominator cap C cap D end-fraction equals the fraction with numerator cap A cap M and denominator cap A cap D end-fraction𝑀𝑃𝐶𝐷=𝐴𝑀𝐴𝐷.
- Ta có AD=AM+MD=AM+2MA=3MAcap A cap D equals cap A cap M plus cap M cap D equals cap A cap M plus 2 cap M cap A equals 3 cap M cap A𝐴𝐷=𝐴𝑀+𝑀𝐷=𝐴𝑀+2𝑀𝐴=3𝑀𝐴.
- Suy ra AMAD=AM3MA=13the fraction with numerator cap A cap M and denominator cap A cap D end-fraction equals the fraction with numerator cap A cap M and denominator 3 cap M cap A end-fraction equals 1 over 3 end-fraction𝐴𝑀𝐴𝐷=𝐴𝑀3𝑀𝐴=13.
- Thay vào biểu thức trên, ta có MP6=13the fraction with numerator cap M cap P and denominator 6 end-fraction equals 1 over 3 end-fraction𝑀𝑃6=13.
- Tính độ dài MPcap M cap P𝑀𝑃: MP=13×6=2cmcap M cap P equals 1 over 3 end-fraction cross 6 equals 2 cm𝑀𝑃=13×6=2cm.
- Áp dụng định lý Thales cho tam giác ABCcap A cap B cap C𝐴𝐵𝐶với PN//ABcap P cap N / / cap A cap B𝑃𝑁//𝐴𝐵, ta có PNAB=CNCBthe fraction with numerator cap P cap N and denominator cap A cap B end-fraction equals the fraction with numerator cap C cap N and denominator cap C cap B end-fraction𝑃𝑁𝐴𝐵=𝐶𝑁𝐶𝐵.
- Từ AMMD=BNNC=12the fraction with numerator cap A cap M and denominator cap M cap D end-fraction equals the fraction with numerator cap B cap N and denominator cap N cap C end-fraction equals 1 over 2 end-fraction𝐴𝑀𝑀𝐷=𝐵𝑁𝑁𝐶=12, suy ra NCBN=2the fraction with numerator cap N cap C and denominator cap B cap N end-fraction equals 2𝑁𝐶𝐵𝑁=2.
- Ta có CB=CN+NB=2BN+BN=3BNcap C cap B equals cap C cap N plus cap N cap B equals 2 cap B cap N plus cap B cap N equals 3 cap B cap N𝐶𝐵=𝐶𝑁+𝑁𝐵=2𝐵𝑁+𝐵𝑁=3𝐵𝑁.
- Suy ra CNCB=2BN3BN=23the fraction with numerator cap C cap N and denominator cap C cap B end-fraction equals the fraction with numerator 2 cap B cap N and denominator 3 cap B cap N end-fraction equals 2 over 3 end-fraction𝐶𝑁𝐶𝐵=2𝐵𝑁3𝐵𝑁=23.
- Thay vào biểu thức trên, ta có PN4=23the fraction with numerator cap P cap N and denominator 4 end-fraction equals 2 over 3 end-fraction𝑃𝑁4=23.
- Tính độ dài PNcap P cap N𝑃𝑁: PN=23×4=83cmcap P cap N equals 2 over 3 end-fraction cross 4 equals 8 over 3 end-fraction cm𝑃𝑁=23×4=83cm.
- Tính độ dài MNcap M cap N𝑀𝑁: MN=MP+PN=2+83=63+83=143cmcap M cap N equals cap M cap P plus cap P cap N equals 2 plus 8 over 3 end-fraction equals 6 over 3 end-fraction plus 8 over 3 end-fraction equals 14 over 3 end-fraction cm𝑀𝑁=𝑀𝑃+𝑃𝑁=2+83=63+83=143cm
2025-12-15 19:22:49
a) Chứng minh AMMD=BNNCthe fraction with numerator cap A cap M and denominator cap M cap D end-fraction equals the fraction with numerator cap B cap N and denominator cap N cap C end-fraction𝐴𝑀𝑀𝐷=𝐵𝑁𝑁𝐶
- Xét tam giác ADCcap A cap D cap C𝐴𝐷𝐶có MPcap M cap P𝑀𝑃song song với CDcap C cap D𝐶𝐷.
- Theo định lý Thales, tỉ số AMMDthe fraction with numerator cap A cap M and denominator cap M cap D end-fraction𝐴𝑀𝑀𝐷bằng APPCthe fraction with numerator cap A cap P and denominator cap P cap C end-fraction𝐴𝑃𝑃𝐶.
- Xét tam giác ABCcap A cap B cap C𝐴𝐵𝐶có PNcap P cap N𝑃𝑁song song với ABcap A cap B𝐴𝐵.
- Theo định lý Thales, tỉ số BNNCthe fraction with numerator cap B cap N and denominator cap N cap C end-fraction𝐵𝑁𝑁𝐶bằng APPCthe fraction with numerator cap A cap P and denominator cap P cap C end-fraction𝐴𝑃𝑃𝐶.
- Từ hai điều trên, suy ra AMMD=BNNCthe fraction with numerator cap A cap M and denominator cap M cap D end-fraction equals the fraction with numerator cap B cap N and denominator cap N cap C end-fraction𝐴𝑀𝑀𝐷=𝐵𝑁𝑁𝐶.
- Từ giả thiết MD=2MAcap M cap D equals 2 cap M cap A𝑀𝐷=2𝑀𝐴, suy ra AMMD=12the fraction with numerator cap A cap M and denominator cap M cap D end-fraction equals 1 over 2 end-fraction𝐴𝑀𝑀𝐷=12.
- Áp dụng định lý Thales cho tam giác ADCcap A cap D cap C𝐴𝐷𝐶với MP//CDcap M cap P / / cap C cap D𝑀𝑃//𝐶𝐷, ta có MPCD=AMADthe fraction with numerator cap M cap P and denominator cap C cap D end-fraction equals the fraction with numerator cap A cap M and denominator cap A cap D end-fraction𝑀𝑃𝐶𝐷=𝐴𝑀𝐴𝐷.
- Ta có AD=AM+MD=AM+2MA=3MAcap A cap D equals cap A cap M plus cap M cap D equals cap A cap M plus 2 cap M cap A equals 3 cap M cap A𝐴𝐷=𝐴𝑀+𝑀𝐷=𝐴𝑀+2𝑀𝐴=3𝑀𝐴.
- Suy ra AMAD=AM3MA=13the fraction with numerator cap A cap M and denominator cap A cap D end-fraction equals the fraction with numerator cap A cap M and denominator 3 cap M cap A end-fraction equals 1 over 3 end-fraction𝐴𝑀𝐴𝐷=𝐴𝑀3𝑀𝐴=13.
- Thay vào biểu thức trên, ta có MP6=13the fraction with numerator cap M cap P and denominator 6 end-fraction equals 1 over 3 end-fraction𝑀𝑃6=13.
- Tính độ dài MPcap M cap P𝑀𝑃: MP=13×6=2cmcap M cap P equals 1 over 3 end-fraction cross 6 equals 2 cm𝑀𝑃=13×6=2cm.
- Áp dụng định lý Thales cho tam giác ABCcap A cap B cap C𝐴𝐵𝐶với PN//ABcap P cap N / / cap A cap B𝑃𝑁//𝐴𝐵, ta có PNAB=CNCBthe fraction with numerator cap P cap N and denominator cap A cap B end-fraction equals the fraction with numerator cap C cap N and denominator cap C cap B end-fraction𝑃𝑁𝐴𝐵=𝐶𝑁𝐶𝐵.
- Từ AMMD=BNNC=12the fraction with numerator cap A cap M and denominator cap M cap D end-fraction equals the fraction with numerator cap B cap N and denominator cap N cap C end-fraction equals 1 over 2 end-fraction𝐴𝑀𝑀𝐷=𝐵𝑁𝑁𝐶=12, suy ra NCBN=2the fraction with numerator cap N cap C and denominator cap B cap N end-fraction equals 2𝑁𝐶𝐵𝑁=2.
- Ta có CB=CN+NB=2BN+BN=3BNcap C cap B equals cap C cap N plus cap N cap B equals 2 cap B cap N plus cap B cap N equals 3 cap B cap N𝐶𝐵=𝐶𝑁+𝑁𝐵=2𝐵𝑁+𝐵𝑁=3𝐵𝑁.
- Suy ra CNCB=2BN3BN=23the fraction with numerator cap C cap N and denominator cap C cap B end-fraction equals the fraction with numerator 2 cap B cap N and denominator 3 cap B cap N end-fraction equals 2 over 3 end-fraction𝐶𝑁𝐶𝐵=2𝐵𝑁3𝐵𝑁=23.
- Thay vào biểu thức trên, ta có PN4=23the fraction with numerator cap P cap N and denominator 4 end-fraction equals 2 over 3 end-fraction𝑃𝑁4=23.
- Tính độ dài PNcap P cap N𝑃𝑁: PN=23×4=83cmcap P cap N equals 2 over 3 end-fraction cross 4 equals 8 over 3 end-fraction cm𝑃𝑁=23×4=83cm.
- Tính độ dài MNcap M cap N𝑀𝑁: MN=MP+PN=2+83=63+83=143cmcap M cap N equals cap M cap P plus cap P cap N equals 2 plus 8 over 3 end-fraction equals 6 over 3 end-fraction plus 8 over 3 end-fraction equals 14 over 3 end-fraction cm𝑀𝑁=𝑀𝑃+𝑃𝑁=2+83=63+83=143cm
2025-12-15 19:22:42
a) Chứng minh AMMD=BNNCthe fraction with numerator cap A cap M and denominator cap M cap D end-fraction equals the fraction with numerator cap B cap N and denominator cap N cap C end-fraction𝐴𝑀𝑀𝐷=𝐵𝑁𝑁𝐶
- Xét tam giác ADCcap A cap D cap C𝐴𝐷𝐶có MPcap M cap P𝑀𝑃song song với CDcap C cap D𝐶𝐷.
- Theo định lý Thales, tỉ số AMMDthe fraction with numerator cap A cap M and denominator cap M cap D end-fraction𝐴𝑀𝑀𝐷bằng APPCthe fraction with numerator cap A cap P and denominator cap P cap C end-fraction𝐴𝑃𝑃𝐶.
- Xét tam giác ABCcap A cap B cap C𝐴𝐵𝐶có PNcap P cap N𝑃𝑁song song với ABcap A cap B𝐴𝐵.
- Theo định lý Thales, tỉ số BNNCthe fraction with numerator cap B cap N and denominator cap N cap C end-fraction𝐵𝑁𝑁𝐶bằng APPCthe fraction with numerator cap A cap P and denominator cap P cap C end-fraction𝐴𝑃𝑃𝐶.
- Từ hai điều trên, suy ra AMMD=BNNCthe fraction with numerator cap A cap M and denominator cap M cap D end-fraction equals the fraction with numerator cap B cap N and denominator cap N cap C end-fraction𝐴𝑀𝑀𝐷=𝐵𝑁𝑁𝐶.
- Từ giả thiết MD=2MAcap M cap D equals 2 cap M cap A𝑀𝐷=2𝑀𝐴, suy ra AMMD=12the fraction with numerator cap A cap M and denominator cap M cap D end-fraction equals 1 over 2 end-fraction𝐴𝑀𝑀𝐷=12.
- Áp dụng định lý Thales cho tam giác ADCcap A cap D cap C𝐴𝐷𝐶với MP//CDcap M cap P / / cap C cap D𝑀𝑃//𝐶𝐷, ta có MPCD=AMADthe fraction with numerator cap M cap P and denominator cap C cap D end-fraction equals the fraction with numerator cap A cap M and denominator cap A cap D end-fraction𝑀𝑃𝐶𝐷=𝐴𝑀𝐴𝐷.
- Ta có AD=AM+MD=AM+2MA=3MAcap A cap D equals cap A cap M plus cap M cap D equals cap A cap M plus 2 cap M cap A equals 3 cap M cap A𝐴𝐷=𝐴𝑀+𝑀𝐷=𝐴𝑀+2𝑀𝐴=3𝑀𝐴.
- Suy ra AMAD=AM3MA=13the fraction with numerator cap A cap M and denominator cap A cap D end-fraction equals the fraction with numerator cap A cap M and denominator 3 cap M cap A end-fraction equals 1 over 3 end-fraction𝐴𝑀𝐴𝐷=𝐴𝑀3𝑀𝐴=13.
- Thay vào biểu thức trên, ta có MP6=13the fraction with numerator cap M cap P and denominator 6 end-fraction equals 1 over 3 end-fraction𝑀𝑃6=13.
- Tính độ dài MPcap M cap P𝑀𝑃: MP=13×6=2cmcap M cap P equals 1 over 3 end-fraction cross 6 equals 2 cm𝑀𝑃=13×6=2cm.
- Áp dụng định lý Thales cho tam giác ABCcap A cap B cap C𝐴𝐵𝐶với PN//ABcap P cap N / / cap A cap B𝑃𝑁//𝐴𝐵, ta có PNAB=CNCBthe fraction with numerator cap P cap N and denominator cap A cap B end-fraction equals the fraction with numerator cap C cap N and denominator cap C cap B end-fraction𝑃𝑁𝐴𝐵=𝐶𝑁𝐶𝐵.
- Từ AMMD=BNNC=12the fraction with numerator cap A cap M and denominator cap M cap D end-fraction equals the fraction with numerator cap B cap N and denominator cap N cap C end-fraction equals 1 over 2 end-fraction𝐴𝑀𝑀𝐷=𝐵𝑁𝑁𝐶=12, suy ra NCBN=2the fraction with numerator cap N cap C and denominator cap B cap N end-fraction equals 2𝑁𝐶𝐵𝑁=2.
- Ta có CB=CN+NB=2BN+BN=3BNcap C cap B equals cap C cap N plus cap N cap B equals 2 cap B cap N plus cap B cap N equals 3 cap B cap N𝐶𝐵=𝐶𝑁+𝑁𝐵=2𝐵𝑁+𝐵𝑁=3𝐵𝑁.
- Suy ra CNCB=2BN3BN=23the fraction with numerator cap C cap N and denominator cap C cap B end-fraction equals the fraction with numerator 2 cap B cap N and denominator 3 cap B cap N end-fraction equals 2 over 3 end-fraction𝐶𝑁𝐶𝐵=2𝐵𝑁3𝐵𝑁=23.
- Thay vào biểu thức trên, ta có PN4=23the fraction with numerator cap P cap N and denominator 4 end-fraction equals 2 over 3 end-fraction𝑃𝑁4=23.
- Tính độ dài PNcap P cap N𝑃𝑁: PN=23×4=83cmcap P cap N equals 2 over 3 end-fraction cross 4 equals 8 over 3 end-fraction cm𝑃𝑁=23×4=83cm.
- Tính độ dài MNcap M cap N𝑀𝑁: MN=MP+PN=2+83=63+83=143cmcap M cap N equals cap M cap P plus cap P cap N equals 2 plus 8 over 3 end-fraction equals 6 over 3 end-fraction plus 8 over 3 end-fraction equals 14 over 3 end-fraction cm𝑀𝑁=𝑀𝑃+𝑃𝑁=2+83=63+83=143cm
2025-12-15 19:22:26
a) Chứng minh AMMD=BNNCthe fraction with numerator cap A cap M and denominator cap M cap D end-fraction equals the fraction with numerator cap B cap N and denominator cap N cap C end-fraction𝐴𝑀𝑀𝐷=𝐵𝑁𝑁𝐶
- Xét tam giác ADCcap A cap D cap C𝐴𝐷𝐶có MPcap M cap P𝑀𝑃song song với CDcap C cap D𝐶𝐷.
- Theo định lý Thales, tỉ số AMMDthe fraction with numerator cap A cap M and denominator cap M cap D end-fraction𝐴𝑀𝑀𝐷bằng APPCthe fraction with numerator cap A cap P and denominator cap P cap C end-fraction𝐴𝑃𝑃𝐶.
- Xét tam giác ABCcap A cap B cap C𝐴𝐵𝐶có PNcap P cap N𝑃𝑁song song với ABcap A cap B𝐴𝐵.
- Theo định lý Thales, tỉ số BNNCthe fraction with numerator cap B cap N and denominator cap N cap C end-fraction𝐵𝑁𝑁𝐶bằng APPCthe fraction with numerator cap A cap P and denominator cap P cap C end-fraction𝐴𝑃𝑃𝐶.
- Từ hai điều trên, suy ra AMMD=BNNCthe fraction with numerator cap A cap M and denominator cap M cap D end-fraction equals the fraction with numerator cap B cap N and denominator cap N cap C end-fraction𝐴𝑀𝑀𝐷=𝐵𝑁𝑁𝐶.
- Từ giả thiết MD=2MAcap M cap D equals 2 cap M cap A𝑀𝐷=2𝑀𝐴, suy ra AMMD=12the fraction with numerator cap A cap M and denominator cap M cap D end-fraction equals 1 over 2 end-fraction𝐴𝑀𝑀𝐷=12.
- Áp dụng định lý Thales cho tam giác ADCcap A cap D cap C𝐴𝐷𝐶với MP//CDcap M cap P / / cap C cap D𝑀𝑃//𝐶𝐷, ta có MPCD=AMADthe fraction with numerator cap M cap P and denominator cap C cap D end-fraction equals the fraction with numerator cap A cap M and denominator cap A cap D end-fraction𝑀𝑃𝐶𝐷=𝐴𝑀𝐴𝐷.
- Ta có AD=AM+MD=AM+2MA=3MAcap A cap D equals cap A cap M plus cap M cap D equals cap A cap M plus 2 cap M cap A equals 3 cap M cap A𝐴𝐷=𝐴𝑀+𝑀𝐷=𝐴𝑀+2𝑀𝐴=3𝑀𝐴.
- Suy ra AMAD=AM3MA=13the fraction with numerator cap A cap M and denominator cap A cap D end-fraction equals the fraction with numerator cap A cap M and denominator 3 cap M cap A end-fraction equals 1 over 3 end-fraction𝐴𝑀𝐴𝐷=𝐴𝑀3𝑀𝐴=13.
- Thay vào biểu thức trên, ta có MP6=13the fraction with numerator cap M cap P and denominator 6 end-fraction equals 1 over 3 end-fraction𝑀𝑃6=13.
- Tính độ dài MPcap M cap P𝑀𝑃: MP=13×6=2cmcap M cap P equals 1 over 3 end-fraction cross 6 equals 2 cm𝑀𝑃=13×6=2cm.
- Áp dụng định lý Thales cho tam giác ABCcap A cap B cap C𝐴𝐵𝐶với PN//ABcap P cap N / / cap A cap B𝑃𝑁//𝐴𝐵, ta có PNAB=CNCBthe fraction with numerator cap P cap N and denominator cap A cap B end-fraction equals the fraction with numerator cap C cap N and denominator cap C cap B end-fraction𝑃𝑁𝐴𝐵=𝐶𝑁𝐶𝐵.
- Từ AMMD=BNNC=12the fraction with numerator cap A cap M and denominator cap M cap D end-fraction equals the fraction with numerator cap B cap N and denominator cap N cap C end-fraction equals 1 over 2 end-fraction𝐴𝑀𝑀𝐷=𝐵𝑁𝑁𝐶=12, suy ra NCBN=2the fraction with numerator cap N cap C and denominator cap B cap N end-fraction equals 2𝑁𝐶𝐵𝑁=2.
- Ta có CB=CN+NB=2BN+BN=3BNcap C cap B equals cap C cap N plus cap N cap B equals 2 cap B cap N plus cap B cap N equals 3 cap B cap N𝐶𝐵=𝐶𝑁+𝑁𝐵=2𝐵𝑁+𝐵𝑁=3𝐵𝑁.
- Suy ra CNCB=2BN3BN=23the fraction with numerator cap C cap N and denominator cap C cap B end-fraction equals the fraction with numerator 2 cap B cap N and denominator 3 cap B cap N end-fraction equals 2 over 3 end-fraction𝐶𝑁𝐶𝐵=2𝐵𝑁3𝐵𝑁=23.
- Thay vào biểu thức trên, ta có PN4=23the fraction with numerator cap P cap N and denominator 4 end-fraction equals 2 over 3 end-fraction𝑃𝑁4=23.
- Tính độ dài PNcap P cap N𝑃𝑁: PN=23×4=83cmcap P cap N equals 2 over 3 end-fraction cross 4 equals 8 over 3 end-fraction cm𝑃𝑁=23×4=83cm.
- Tính độ dài MNcap M cap N𝑀𝑁: MN=MP+PN=2+83=63+83=143cmcap M cap N equals cap M cap P plus cap P cap N equals 2 plus 8 over 3 end-fraction equals 6 over 3 end-fraction plus 8 over 3 end-fraction equals 14 over 3 end-fraction cm𝑀𝑁=𝑀𝑃+𝑃𝑁=2+83=63+83=143cm