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$解：??(1)△ADE∽△ABC，????△AFE∽△ADC，????△FDE∽△DBC??$

$∵??DE//BC??$

$∴??∠ADE=∠ABC??$

$∵??∠A=∠A??$

$∴??△ADE∽△ABC??$（更多請點擊查看作業(yè)精靈詳解）

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$解：??(2)??∵??DE//FG//BC??$

$∴??△ADE∽△AFG??$

$∴??\frac {DE}{FG}=\frac {AE}{AG}??$

$∵??DE=2，????FG=3，????AE=4??$

$∴??\frac 23=\frac 4{AG}??$

$∴??AG=6，????EG=2??$

$同理可得，??CG=4??$

$∵??EG=DE??$

$∴??∠EGD=∠EDG??$

$∵??DE//BC??$

$∴??∠EDG=∠H??$

$∵??∠EGD=∠CGH??$

$∴??∠CGH=∠H??$

$∴??CH=CG=4??$

（更多請點擊查看作業(yè)精靈詳解）

$解：作??DG//AF{交}BC??于點??G??$

$∵??DG//AF??$

$∴??\frac {AD}{CD}=\frac {FG}{CG}，????\frac {BE}{ED}=\frac {BF}{FG}??$

$∵??\frac {AD}{CD}=\frac 23，????\frac {BE}{ED}=\frac 32??$

$∴??\frac {FG}{CG}=\frac 23，????\frac {BF}{FG}=\frac 32??$

$設(shè)??FG=2x，??則??CG=3x，????BF=3x??$

$∴??FC=FG+CG=5x??$

$∴??BF：????FC=3：????5??$

$解:??(2)??∵??△ADE∽△ABC?? $

$∴??\frac {AE}{AC}=\frac {DE}{BC}??$

$∵??AE=5，????EC=3，????BC=7??$

$∴??AC=AE+EC=8??$

$∴??\frac 58=\frac {DE}7??$

$∴??DE=\frac {35}{8}??$

$∵??EF//CD??$

$∴??△AFE∽△ADC??$

$∴??\frac {AE}{AC}=\frac {EF}{CD}，??即??\frac 58=\frac 4{CD}??$

$∴??CD=\frac {32}{5}??$

$解：取??CG ??的中點??H，??連接??EH??$

$∵??DE??是??△ABC??的中位線$

$∴??E??是??AC??的中點$

$∵??H??是??CG ??的中點$

$∴??EH??是??△ACG??的中位線$

$∴??EH//AG，????AG=2HE??$

$∴??∠GDF=∠HEF??$

$∵??F ??是??DE??的中點$

$∴??DF=EF??$

$在??△DFG ??和??△EFH??中$

$??\begin{cases}{∠GDF=∠HEF}\\{DF=EF}\\{∠GFD=∠HFE}\end{cases}??$

$∴??△DFG≌△EFH(\mathrm {ASA})??$

$∴??GD=HE??$

$∴??AG：????GD=2HE：????HE=2：????1??$

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