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電子課本網(wǎng) › 第41頁

第41頁

信息發(fā)布者：

$ \frac {EF}{FG}$

$ \frac {AD}{BD}$

12

2：3

6

證明：∵?$EG//BC$?

∴?$\frac {AE}{AB}=\frac {AG}{AC}$?

∵?$GF//CD$?

∴?$\frac {AF}{AD}=\frac {AG}{AC}$?

∴?$\frac {AE}{AB}=\frac {AF}{AD}$?

1

解：過點(diǎn)?$D$?作?$DF//BE，$?交?$AC$?于點(diǎn)?$F$?

∵?$DF//BE$?

∴?$\frac {CF}{CE}=\frac {CD}{BC}=\frac {1}{2}$?

∴點(diǎn)?$F $?為?$CE$?的中點(diǎn)

∵?$DF//BC$?

∴?$\frac {AO}{AD}=\frac {AE}{AF}$?

?$ (1)$?∵?$\frac {AE}{AC}=\frac {1}{2}$?

∴?$\frac {AE}{AF}=\frac {2}{3}$?

∴?$\frac {AO}{AD}=\frac {2}{3}$?

?$ (2)$?∵?$\frac {AE}{AC}=\frac {1}{3}$?

∴?$\frac {AE}{AF}=\frac {1}{2}$?

∴?$\frac {AO}{AD}=\frac {1}{2}$?

?$ (3)$?∵?$\frac {AE}{AC}=\frac {1}{4}$?

∴?$\frac {AE}{AF}=\frac {2}{5}$?

∴?$\frac {AO}{AD}=\frac {2}{5}$?

?$ (4)$?∵?$\frac {AE}{AC}=\frac {1}{n+1}$?

∴?$\frac {AE}{AF}=\frac {2}{n+2}$?

∴?$\frac {AO}{AD}=\frac {2}{n+2}$?

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